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Perfect number

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Jump to navigationJump to searchFor the 2012 film, see Perfect Number (film).

Illustration of the perfect number status of the number 6

In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number.

The sum of divisors of a number, excluding the number itself, is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors including itself; in symbols, σ1(n) = 2n where σ1 is the sum-of-divisors function. For instance, 28 is perfect as 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 × 28.

This definition is ancient, appearing as early as Euclid's Elements (VII.22) where it is called τέλειος ἀριθμός (perfect, ideal, or complete number). Euclid also proved a formation rule (IX.36) whereby {\displaystyle q(q+1)/2} is an even perfect number whenever {\displaystyle q} is a prime of the form {\displaystyle 2^{p}-1} for positive integer {\displaystyle p} —what is now called a Mersenne prime. Two millennia later, Leonhard Euler proved that all even perfect numbers are of this form.[1] This is known as the Euclid–Euler theorem.

It is not known whether there are any odd perfect numbers, nor whether infinitely many perfect numbers exist. The first few perfect numbers are 6, 28, 496 and 8128 (sequence A000396 in the OEIS).

Contents

1History

2Even perfect numbers

3Odd perfect numbers

4Minor results

5Related concepts

6See also

7Notes

8References

9Further reading

10External links

History[edit]

In about 300 BC Euclid showed that if 2p − 1 is prime then 2p−1(2p − 1) is perfect. The first four perfect numbers were the only ones known to early Greek mathematics, and the mathematician Nicomachus noted 8128 as early as around AD 100.[2] In modern language, Nicomachus states without proof that every perfect number is of the form {\displaystyle 2^{n-1}(2^{n}-1)} where {\displaystyle 2^{n}-1} is prime.[3][4] He seems to be unaware that n itself has to be prime. He also says (wrongly) that the perfect numbers end in 6 or 8 alternately. (The first 5 perfect numbers end with digits 6, 8, 6, 8, 6; but the sixth also ends in 6.) Philo of Alexandria in his first-century book "On the creation" mentions perfect numbers, claiming that the world was created in 6 days and the moon orbits in 28 days because 6 and 28 are perfect. Philo is followed by Origen,[5] and by Didymus the Blind, who adds the observation that there are only four perfect numbers that are less than 10,000. (Commentary on Genesis 1. 14–19).[6] St Augustine defines perfect numbers in City of God (Book XI, Chapter 30) in the early 5th century AD, repeating the claim that God created the world in 6 days because 6 is the smallest perfect number. The Egyptian mathematician Ismail ibn Fallūs (1194–1252) mentioned the next three perfect numbers (33,550,336; 8,589,869,056; and 137,438,691,328) and listed a few more which are now known to be incorrect.[7] The first known European mention of the fifth perfect number is a manuscript written between 1456 and 1461 by an unknown mathematician.[8] In 1588, the Italian mathematician Pietro Cataldi identified the sixth (8,589,869,056) and the seventh (137,438,691,328) perfect numbers, and also proved that every perfect number obtained from Euclid's rule ends with a 6 or an 8.[9][10][11]

Even perfect numbers[edit]

See also: Euclid–Euler theorem

Unsolved problem in mathematics:

Are there infinitely many perfect numbers?

(more unsolved problems in mathematics)

Euclid proved that 2p−1(2p − 1) is an even perfect number whenever 2p − 1 is prime (Elements, Prop. IX.36).

For example, the first four perfect numbers are generated by the formula 2p−1(2p − 1), with p a prime number, as follows:

for p = 2: 21(22 − 1) = 2 × 3 = 6

for p = 3: 22(23 − 1) = 4 × 7 = 28

for p = 5: 24(25 − 1) = 16 × 31 = 496

for p = 7: 26(27 − 1) = 64 × 127 = 8128.

Prime numbers of the form 2p − 1 are known as Mersenne primes, after the seventeenth-century monk Marin Mersenne, who studied number theory and perfect numbers. For 2p − 1 to be prime, it is necessary that p itself be prime. However, not all numbers of the form 2p − 1 with a prime p are prime; for example, 211 − 1 = 2047 = 23 × 89 is not a prime number.[12] In fact, Mersenne primes are very rare—of the 2,610,944 prime numbers p up to 43,112,609,[13] 2p − 1 is prime for only 47 of them.

Although Nicomachus had stated (without proof) that all perfect numbers were of the form {\displaystyle 2^{n-1}\left(2^{n}-1\right)} where {\displaystyle 2^{n}-1} is prime (though he stated this somewhat differently), Ibn al-Haytham (Alhazen) circa AD 1000 conjectured only that every even perfect number is of that form.[14] It was not until the 18th century that Leonhard Euler proved that the formula 2p−1(2p − 1) will yield all the even perfect numbers. Thus, there is a one-to-one correspondence between even perfect numbers and Mersenne primes; each Mersenne prime generates one even perfect number, and vice versa. This result is often referred to as the Euclid–Euler theorem.

An exhaustive search by the GIMPS distributed computing project has shown that the first 48 even perfect numbers are 2p−1(2p − 1) for

p = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609 and 57885161 (sequence A000043 in the OEIS).[15]

Three higher perfect numbers have also been discovered, namely those for which p = 74207281, 77232917, and 82589933, though there may be others within this range. As of December 2018, 51 Mersenne primes are known,[16] and therefore 51 even perfect numbers (the largest of which is 282589932 × (282589933 − 1) with 49,724,095 digits). It is not known whether there are infinitely many perfect numbers, nor whether there are infinitely many Mersenne primes.

As well as having the form 2p−1(2p − 1), each even perfect number is the (2p − 1)th triangular number (and hence equal to the sum of the integers from 1 to 2p − 1) and the 2p−1th hexagonal number. Furthermore, each even perfect number except for 6 is the ((2p + 1)/3)th centered nonagonal number and is equal to the sum of the first 2(p−1)/2 odd cubes:

{\displaystyle {\begin{aligned}6=2^{1}\left(2^{2}-1\right)&=1+2+3,\\[8pt]28=2^{2}\left(2^{3}-1\right)&=1+2+3+4+5+6+7=1^{3}+3^{3},\\[8pt]496=2^{4}\left(2^{5}-1\right)&=1+2+3+\cdots +29+30+31\\&=1^{3}+3^{3}+5^{3}+7^{3},\\[8pt]8128=2^{6}\left(2^{7}-1\right)&=1+2+3+\cdots +125+126+127\\&=1^{3}+3^{3}+5^{3}+7^{3}+9^{3}+11^{3}+13^{3}+15^{3},\\[8pt]33550336=2^{12}\left(2^{13}-1\right)&=1+2+3+\cdots +8189+8190+8191\\&=1^{3}+3^{3}+5^{3}+\cdots +123^{3}+125^{3}+127^{3}.\end{aligned}}}

Even perfect numbers (except 6) are of the form

{\displaystyle T_{2^{p}-1}=1+{\frac {\left(2^{p}-2\right)\times \left(2^{p}+1\right)}{2}}=1+9\times T_{\left(2^{p}-2\right)/3}}

with each resulting triangular number T7 = 28, T31 = 496, T127 = 8128 (after subtracting 1 from the perfect number and dividing the result by 9) ending in 3 or 5, the sequence starting with T2 = 3, T10 = 55, T42 = 903, T2730 = 3727815, ...[17] This can be reformulated as follows: adding the digits of any even perfect number (except 6), then adding the digits of the resulting number, and repeating this process until a single digit (called the digital root) is obtained, always produces the number 1. For example, the digital root of 8128 is 1, because 8 + 1 + 2 + 8 = 19, 1 + 9 = 10, and 1 + 0 = 1. This works with all perfect numbers 2p−1(2p − 1) with odd prime p and, in fact, with all numbers of the form 2m−1(2m − 1) for odd integer (not necessarily prime) m.

Owing to their form, 2p−1(2p − 1), every even perfect number is represented in binary form as p ones followed by p − 1 zeros; for example,

610 = 22 + 21 = 1102,

2810 = 24 + 23 + 22 = 111002,

49610 = 28 + 27 + 26 + 25 + 24 = 1111100002, and

812810 = 212 + 211 + 210 + 29 + 28 + 27 + 26 = 11111110000002.

Thus every even perfect number is a pernicious number.

Every even perfect number is also a practical number (cf. Related concepts).

Odd perfect numbers[edit]

Unsolved problem in mathematics:

Are there any odd perfect numbers?

(more unsolved problems in mathematics)

It is unknown whether any odd perfect numbers exist, though various results have been obtained. In 1496, Jacques Lefèvre stated that Euclid's rule gives all perfect numbers,[18] thus implying that no odd perfect number exists. Euler stated: "Whether ... there are any odd perfect numbers is a most difficult question".[19] More recently, Carl Pomerance has presented a heuristic argument suggesting that indeed no odd perfect number should exist.[20] All perfect numbers are also Ore's harmonic numbers, and it has been conjectured as well that there are no odd Ore's harmonic numbers other than 1.

Any odd perfect number N must satisfy the following conditions:

N > 101500.[21]

N is not divisible by 105.[22]

N is of the form N ≡ 1 (mod 12) or N ≡ 117 (mod 468) or N ≡ 81 (mod 324).[23]

N is of the form

{\displaystyle N=q^{\alpha }p_{1}^{2e_{1}}\cdots p_{k}^{2e_{k}},}

where:q, p1, ..., pk are distinct odd primes (Euler).

q ≡ α ≡ 1 (mod 4) (Euler).

The smallest prime factor of N is at most {\displaystyle {\frac {k-1}{2}}.} [24]

Either qα > 1062, or pj2ej > 1062 for some j.[21]

{\displaystyle N<2^{(4^{k+1}-2^{k+1})}} [25][26]

{\displaystyle \alpha +2e_{1}+2e_{2}+2e_{3}+\cdots +2e_{k}\geq {\frac {66k-191}{25}}} .[24][27]

{\displaystyle qp_{1}p_{2}p_{3}\cdots p_{k}<2N^{\frac {17}{26}}} .[28]

The largest prime factor of N is greater than 108[29] and less than {\displaystyle (3N)^{1/3}.} [30]

The second largest prime factor is greater than 104,[31] and is less than {\displaystyle (2N)^{1/5}} .[32]

The third largest prime factor is greater than 100,[33] and less than {\displaystyle (2N)^{\frac {1}{6}}.} [34]

N has at least 101 prime factors and at least 10 distinct prime factors.[21][35] If 3 is not one of the factors of N, then N has at least 12 distinct prime factors.[36]

Furthermore, several minor results are known about the exponents e1, ..., ek.

Not all ei ≡ 1 (mod 3).[37]

Not all ei ≡ 2 (mod 5).[38]

If all ei ≡ 1 (mod 3) or 2 (mod 5), then the smallest prime factor of N must lie between 108 and 101000.[38]

More generally, if all 2ei+1 have a prime factor in a given finite set S, then the smallest prime factor of N must be smaller than an effectively computable constant depending only on S.[38]

If (e1, ..., ek)= (1, ..., 1, 2, ..., 2) with t ones and u twos, then {\displaystyle (t-1)/4\leq u\leq 2t+{\sqrt {\alpha }}} .[39]

(e1, ..., ek) ≠ (1, ..., 1, 3),[40] (1, ..., 1, 5), (1, ..., 1, 6).[41]

If e1 = ... = ek = e, thene cannot be 3,[42] 5, 24,[43] 6, 8, 11, 14 or 18.[41]

{\displaystyle k\leq 2e^{2}+8e+2} and {\displaystyle N<2^{4^{2e^{2}+8e+3}}} .[44]

In 1888, Sylvester stated:[45]

... a prolonged meditation on the subject has satisfied me that the existence of any one such [odd perfect number]—its escape, so to say, from the complex web of conditions which hem it in on all sides—would be little short of a miracle.

Many of the properties proved about odd perfect numbers also apply to Descartes numbers, and Pace Nielsen has suggested that sufficient study of those numbers may lead to a proof that no odd perfect numbers exist.[46]

Minor results[edit]

All even perfect numbers have a very precise form; odd perfect numbers either do not exist or are rare. There are a number of results on perfect numbers that are actually quite easy to prove but nevertheless superficially impressive; some of them also come under Richard Guy's strong law of small numbers:

The only even perfect number of the form x3 + 1 is 28 (Makowski 1962).[47]

28 is also the only even perfect number that is a sum of two positive cubes of integers (Gallardo 2010).[48]

The reciprocals of the divisors of a perfect number N must add up to 2 (to get this, take the definition of a perfect number, {\displaystyle \sigma _{1}(n)=2n} , and divide both sides by n):For 6, we have {\displaystyle 1/6+1/3+1/2+1/1=2} ;

For 28, we have {\displaystyle 1/28+1/14+1/7+1/4+1/2+1/1=2} , etc.

The number of divisors of a perfect number (whether even or odd) must be even, because N cannot be a perfect square.[49]From these two results it follows that every perfect number is an Ore's harmonic number.

The even perfect numbers are not trapezoidal numbers; that is, they cannot be represented as the difference of two positive non-consecutive triangular numbers. There are only three types of non-trapezoidal numbers: even perfect numbers, powers of two, and the numbers of the form {\displaystyle 2^{n-1}(2^{n}+1)} formed as the product of a Fermat prime {\displaystyle 2^{n}+1} with a power of two in a similar way to the construction of even perfect numbers from Mersenne primes.[50]

The number of perfect numbers less than n is less than {\displaystyle c{\sqrt {n}}} , where c > 0 is a constant.[51] In fact it is {\displaystyle o({\sqrt {n}})} , using little-o notation.[52]

Every even perfect number ends in 6 or 28, base ten; and, with the only exception of 6, ends in 1, base 9.[53][54] Therefore, in particular the digital root of every even perfect number other than 6 is 1.

The only square-free perfect number is 6.[55]

Related concepts[edit]

Euler diagram of abundant, primitive abundant, highly abundant, superabundant, colossally abundant, highly composite, superior highly composite, weird and perfect numbers under 100 in relation to deficient and composite numbers

The sum of proper divisors gives various other kinds of numbers. Numbers where the sum is less than the number itself are called deficient, and where it is greater than the number, abundant. These terms, together with perfect itself, come from Greek numerology. A pair of numbers which are the sum of each other's proper divisors are called amicable, and larger cycles of numbers are called sociable. A positive integer such that every smaller positive integer is a sum of distinct divisors of it is a practical number.

By definition, a perfect number is a fixed point of the restricted divisor function s(n) = σ(n) − n, and the aliquot sequence associated with a perfect number is a constant sequence. All perfect numbers are also {\displaystyle {\mathcal {S}}} -perfect numbers, or Granville numbers.

A semiperfect number is a natural number that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number. Most abundant numbers are also semiperfect; abundant numbers which are not semiperfect are called weird numbers.

See also[edit]

Hyperperfect number

Leinster group

List of Mersenne primes and perfect numbers

Multiply perfect number

Superperfect numbers

Unitary perfect number

Harmonic divisor number

Notes[edit]

^ Caldwell, Chris, "A proof that all even perfect numbers are a power of two times a Mersenne prime".

^ Dickson, L. E. (1919). History of the Theory of Numbers, Vol. I. Washington: Carnegie Institution of Washington. p. 4.

^ "Perfect numbers". www-groups.dcs.st-and.ac.uk. Retrieved 9 May 2018.

^ In Introduction to Arithmetic, Chapter 16, he says of perfect numbers, "There is a method of producing them, neat and unfailing, which neither passes by any of the perfect numbers nor fails to differentiate any of those that are not such, which is carried out in the following way." He then goes on to explain a procedure which is equivalent to finding a triangular number based on a Mersenne prime.

^ Commentary on the Gospel of John 28.1.1–4, with further references in the Sources Chrétiennes edition: vol. 385, 58–61.

^ http://torreys.org/sblpapers2015/S22-05_philonic_arithmological_exegesis.pdf

^ Roshdi Rashed, The Development of Arabic Mathematics: Between Arithmetic and Algebra (Dordrecht: Kluwer Academic Publishers, 1994), pp. 328–329.

^ Bayerische Staatsbibliothek, Clm 14908. See David Eugene Smith (1925). History of Mathematics: Volume II. New York: Dover. p. 21. ISBN 0-486-20430-8.

^ Dickson, L. E. (1919). History of the Theory of Numbers, Vol. I. Washington: Carnegie Institution of Washington. p. 10.

^ Pickover, C (2001). Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning. Oxford: Oxford University Press. p. 360. ISBN 0-19-515799-0.

^ Peterson, I (2002). Mathematical Treks: From Surreal Numbers to Magic Circles. Washington: Mathematical Association of America. p. 132. ISBN 88-8358-537-2.

^ All factors of 2p − 1 are congruent to 1 mod 2p. For example, 211 − 1 = 2047 = 23 × 89, and both 23 and 89 yield a remainder of 1 when divided by 11. Furthermore, whenever p is a Sophie Germain prime—that is, 2p + 1 is also prime—and 2p + 1 is congruent to 1 or 7 mod 8, then 2p + 1 will be a factor of 2p − 1, which is the case for p = 11, 23, 83, 131, 179, 191, 239, 251, ... OEIS: A002515.

^ "Number of primes <= 43112609". Wolfram Alpha. Retrieved 2018-10-28.

^ O'Connor, John J.; Robertson, Edmund F., "Abu Ali al-Hasan ibn al-Haytham", MacTutor History of Mathematics archive, University of St Andrews

^ GIMPS Milestones Report. Retrieved 2018-02-27

^ "GIMPS Home". Mersenne.org. Retrieved 2018-12-21.

^ Weisstein, Eric W. "Perfect Number". MathWorld.

^ Dickson, L. E. (1919). History of the Theory of Numbers, Vol. I. Washington: Carnegie Institution of Washington. p. 6.

^ http://www.math.harvard.edu/~knill/seminars/perfect/handout.pdf

^ Oddperfect.org. Archived 2006-12-29 at the Wayback Machine

^ Jump up to:a b c Ochem, Pascal; Rao, Michaël (2012). "Odd perfect numbers are greater than 101500" (PDF). Mathematics of Computation. 81 (279): 1869–1877. doi:10.1090/S0025-5718-2012-02563-4. ISSN 0025-5718. Zbl 1263.11005.

^ Kühnel, Ullrich (1950). "Verschärfung der notwendigen Bedingungen für die Existenz von ungeraden vollkommenen Zahlen". Mathematische Zeitschrift (in German). 52: 202–211. doi:10.1007/BF02230691.

^ Roberts, T (2008). "On the Form of an Odd Perfect Number" (PDF). Australian Mathematical Gazette. 35 (4): 244.

^ Jump up to:a b Zelinsky, Joshua (3 August 2021). "On the Total Number of Prime Factors of an Odd Perfect Number" (PDF). Integers. 21. Retrieved 7 August 2021.

^ Chen, Yong-Gao; Tang, Cui-E (2014). "Improved upper bounds for odd multiperfect numbers". Bulletin of the Australian Mathematical Society. 89 (3): 353–359.

^ Nielsen, Pace P. (2003). "An upper bound for odd perfect numbers". Integers. 3: A14–A22. Retrieved 23 March 2021.

^ Ochem, Pascal; Rao, Michaël (2014). "On the number of prime factors of an odd perfect number". Mathematics of Computation. 83 (289): 2435–2439. doi:10.1090/S0025-5718-2013-02776-7.

^ Pomerance, Carl; Luca, Florian (2010). "On the radical of a perfect number". New York Journal of Mathematics. 16: 23–30. Retrieved 7 December 2018.

^ Goto, T; Ohno, Y (2008). "Odd perfect numbers have a prime factor exceeding 108" (PDF). Mathematics of Computation. 77 (263): 1859–1868. Bibcode:2008MaCom..77.1859G. doi:10.1090/S0025-5718-08-02050-9. Retrieved 30 March 2011.

^ Konyagin, Sergei; Acquaah, Peter (2012). "On Prime Factors of Odd Perfect Numbers". International Journal of Number Theory. 8 (6): 1537–1540. doi:10.1142/S1793042112500935.

^ Iannucci, DE (1999). "The second largest prime divisor of an odd perfect number exceeds ten thousand" (PDF). Mathematics of Computation. 68 (228): 1749–1760. Bibcode:1999MaCom..68.1749I. doi:10.1090/S0025-5718-99-01126-6. Retrieved 30 March 2011.

^ Zelinsky, Joshua (July 2019). "Upper bounds on the second largest prime factor of an odd perfect number". International Journal of Number Theory. 15 (6): 1183–1189. arXiv:1810.11734. doi:10.1142/S1793042119500659..

^ Iannucci, DE (2000). "The third largest prime divisor of an odd perfect number exceeds one hundred" (PDF). Mathematics of Computation. 69 (230): 867–879. Bibcode:2000MaCom..69..867I. doi:10.1090/S0025-5718-99-01127-8. Retrieved 30 March 2011.

^ Bibby, Sean; Vyncke, Pieter; Zelinsky, Joshua (23 November 2021). "On the Third Largest Prime Divisor of an Odd Perfect Number" (PDF). Integers. 21. Retrieved 6 December 2021.

^ Nielsen, Pace P. (2015). "Odd perfect numbers, Diophantine equations, and upper bounds" (PDF). Mathematics of Computation. 84 (295): 2549–2567. doi:10.1090/S0025-5718-2015-02941-X. Retrieved 13 August 2015.

^ Nielsen, Pace P. (2007). "Odd perfect numbers have at least nine distinct prime factors" (PDF). Mathematics of Computation. 76 (260): 2109–2126. arXiv:math/0602485. Bibcode:2007MaCom..76.2109N. doi:10.1090/S0025-5718-07-01990-4. Retrieved 30 March 2011.

^ McDaniel, Wayne L. (1970). "The non-existence of odd perfect numbers of a certain form". Archiv der Mathematik. 21 (1): 52–53. doi:10.1007/BF01220877. ISSN 1420-8938. MR 0258723.

^ Jump up to:a b c Fletcher, S. Adam; Nielsen, Pace P.; Ochem, Pascal (2012). "Sieve methods for odd perfect numbers" (PDF). Mathematics of Computation. 81 (279): 1753?1776. doi:10.1090/S0025-5718-2011-02576-7. ISSN 0025-5718. MR 2904601.

^ Cohen, G. L. (1987). "On the largest component of an odd perfect number". Journal of the Australian Mathematical Society, Series A. 42 (2): 280–286. doi:10.1017/S1446788700028251. ISSN 1446-8107. MR 0869751.

^ Kanold, Hans-Joachim (1950). "Satze uber Kreisteilungspolynome und ihre Anwendungen auf einige zahlentheoretisehe Probleme. II". Journal für die reine und angewandte Mathematik. 188 (1): 129–146. doi:10.1515/crll.1950.188.129. ISSN 1435-5345. MR 0044579.

^ Jump up to:a b Cohen, G. L.; Williams, R. J. (1985). "Extensions of some results concerning odd perfect numbers" (PDF). Fibonacci Quarterly. 23 (1): 70–76. ISSN 0015-0517. MR 0786364.

^ Hagis, Peter Jr.; McDaniel, Wayne L. (1972). "A new result concerning the structure of odd perfect numbers". Proceedings of the American Mathematical Society. 32 (1): 13–15. doi:10.1090/S0002-9939-1972-0292740-5. ISSN 1088-6826. MR 0292740.

^ McDaniel, Wayne L.; Hagis, Peter Jr. (1975). "Some results concerning the non-existence of odd perfect numbers of the form {\displaystyle p^{\alpha }M^{2\beta }} " (PDF). Fibonacci Quarterly. 13 (1): 25–28. ISSN 0015-0517. MR 0354538.

^ Yamada, Tomohiro (2019). "A new upper bound for odd perfect numbers of a special form". Colloquium Mathematicum. 156 (1): 15–21. arXiv:1706.09341. doi:10.4064/cm7339-3-2018. ISSN 1730-6302.

^ The Collected Mathematical Papers of James Joseph Sylvester p. 590, tr. from "Sur les nombres dits de Hamilton", Compte Rendu de l'Association Française (Toulouse, 1887), pp. 164–168.

^ Nadis, Steve (10 September 2020). "Mathematicians Open a New Front on an Ancient Number Problem". Quanta Magazine. Retrieved 10 September 2020.

^ Makowski, A. (1962). "Remark on perfect numbers". Elem. Math. 17 (5): 109.

^ Gallardo, Luis H. (2010). "On a remark of Makowski about perfect numbers". Elem. Math. 65: 121–126. doi:10.4171/EM/149..

^ Yan, Song Y. (2012), Computational Number Theory and Modern Cryptography, John Wiley & Sons, Section 2.3, Exercise 2(6), ISBN 9781118188613.

^ Jones, Chris; Lord, Nick (1999). "Characterising non-trapezoidal numbers". The Mathematical Gazette. The Mathematical Association. 83 (497): 262–263. doi:10.2307/3619053. JSTOR 3619053.

^ Hornfeck, B (1955). "Zur Dichte der Menge der vollkommenen zahlen". Arch. Math. 6 (6): 442–443. doi:10.1007/BF01901120.

^ Kanold, HJ (1956). "Eine Bemerkung ¨uber die Menge der vollkommenen zahlen". Math. Ann. 131 (4): 390–392. doi:10.1007/BF01350108.

^ H. Novarese. Note sur les nombres parfaits Texeira J. VIII (1886), 11–16.

^ Dickson, L. E. (1919). History of the Theory of Numbers, Vol. I. Washington: Carnegie Institution of Washington. p. 25.

^ Redmond, Don (1996). Number Theory: An Introduction to Pure and Applied Mathematics. Chapman & Hall/CRC Pure and Applied Mathematics. 201. CRC Press. Problem 7.4.11, p. 428. ISBN 9780824796969..

References[edit]

Euclid, Elements, Book IX, Proposition 36. See D.E. Joyce's website for a translation and discussion of this proposition and its proof.

Kanold, H.-J. (1941). "Untersuchungen über ungerade vollkommene Zahlen". Journal für die Reine und Angewandte Mathematik. 183: 98–109.

Steuerwald, R. "Verschärfung einer notwendigen Bedingung für die Existenz einer ungeraden vollkommenen Zahl". S.-B. Bayer. Akad. Wiss. 1937: 69–72.

Further reading[edit]

Nankar, M.L.: "History of perfect numbers," Ganita Bharati 1, no. 1–2 (1979), 7–8.

Hagis, P. (1973). "A Lower Bound for the set of odd Perfect Prime Numbers". Mathematics of Computation. 27 (124): 951–953. doi:10.2307/2005530. JSTOR 2005530.

Riele, H.J.J. "Perfect Numbers and Aliquot Sequences" in H.W. Lenstra and R. Tijdeman (eds.): Computational Methods in Number Theory, Vol. 154, Amsterdam, 1982, pp. 141–157.

Riesel, H. Prime Numbers and Computer Methods for Factorisation, Birkhauser, 1985.

Sándor, Jozsef; Crstici, Borislav (2004). Handbook of number theory II. Dordrecht: Kluwer Academic. pp. 15–98. ISBN 1-4020-2546-7. Zbl 1079.11001.

External links[edit]

"Perfect number", Encyclopedia of Mathematics, EMS Press, 2001 [1994]

David Moews: Perfect, amicable and sociable numbers

Perfect numbers – History and Theory

Weisstein, Eric W. "Perfect Number". MathWorld.

OEIS sequence A000396 (Perfect numbers)

OddPerfect.org A projected distributed computing project to search for odd perfect numbers.

Great Internet Mersenne Prime Search (GIMPS)

Perfect Numbers, math forum at Drexel.

Grimes, James. "8128: Perfect Numbers". Numberphile. Brady Haran. Archived from the original on 2013-05-31. Retrieved 2013-04-02.

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Arthas Menethil

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Jump to navigationJump to search"Lich King" redirects here. For the band, see Lich King (band).

Arthas Menethil

Warcraft character

Arthas Menethil in Heroes of the Storm

First appearance

A Trial of Will, Chapter 5 of Warcraft: Of Blood and Honor

First game

Warcraft III: Reign of Chaos

Created by

Blizzard Entertainment

Voiced by

Justin Gross

Patrick Seitz

Michael McConnohie

Arthas Menethil is a fictional character who appears in the Warcraft series of video games by Blizzard Entertainment. He was once a paladin of the Silver Hand and the crown prince of Lordaeron, but he was corrupted by the cursed blade Frostmourne in a bid to save his people. He later became the Lich King, one of the most prominent antagonists in Warcraft lore. Arthas also appears as a playable character in the crossover multiplayer online battle arena game Heroes of the Storm. The critical reception of the character has been mostly positive.

In Warcraft III, Arthas is voiced by Justin Gross. In subsequent appearances, he is voiced by Patrick Seitz (paladin and death knight Arthas) and Michael McConnohie (Lich King Arthas).

Contents

1Development

2Appearances2.1Warcraft franchise

2.2Heroes of the Storm

2.3Other appearances

3Reception

4References

5External links

Development[edit]

According to Warcraft game designers Scott Mercer and Greg Street, "early on in the development of Warcraft III, we knew the game would be about heroes leading their armies into battle. We initially created Arthas as one of those leaders, so we knew from the beginning he would be central to the storyline", and that he "is the bridge connecting the human and the undead campaigns."[1]

Regarding the development of World of Warcraft: Wrath of the Lich King, Mercer stated that "when development began on Wrath of the Lich King, we knew we wanted the players to have a more personal connection with the Lich King ... so we started designing quests and instances in which we could show the Lich King to the players." Developers also designed the game so that "players can see the wrecks of the Alliance ships that Arthas set ablaze ... they can also find the altar upon which Arthas first discovered Frostmourne ... We deliberately built these aspects into Wrath of the Lich King to help remind players who Arthas is and where he came from, which we hope makes his character that much more vivid in players' minds."[1]

Appearances[edit]

This section may need to be rewritten to comply with Wikipedia's quality standards. You can help. The talk page may contain suggestions. (November 2018)

Warcraft franchise[edit]

Arthas Menethil was the prince of Lordaeron and the only son of Terenas Menethil II. Arthas was an idealistic, yet somewhat rash, young man who dreamed of one day succeeding his father as king of Lordaeron. Arthas became an apprentice paladin at nineteen and served as a favorite pupil of Uther the Lightbringer. Though Arthas loved the kindly Uther like an uncle, he longed to take command of his own destiny and become a hero like the brave veterans who fought the orcs during the Second War. Despite the heartache he felt when his brief affair with the sorceress Jaina Proudmoore came to an end, Arthas remained remarkably committed to his roles as both the prince of Lordaeron and as a holy paladin. He had a deep reverence for the Light and wanted nothing more than to safeguard his beloved people from harm.

Arthas was inducted into Knights of the Silver Hand at the age of 19. The ceremony was held in the Cathedral of Light in Stormwind City, and was attended by prominent figures such as Genn Greymane, Thoras Trollbane, Daelin Proudmoore, and Jaina Proudmoore, whom Arthas had not seen since childhood. Archbishop Alonsus Faol led the initiation process, which included four of the five original paladins: Uther, Tirion Fordring, Saidan Dathrohan, and Gavinrad the Dire. Arthas was presented with the holy warhammer called Light's Vengeance by Gavinrad, and had the ceremonial silver plates placed upon his shoulders by Uther. While in Stormwind, Arthas visited the newly crowned king, Varian Wrynn, and sparred with him while recounting old memories. He also met the recently born prince, Anduin Wrynn, who gripped his finger.

When Arthas took up the fight against the Scourge, he became increasingly frustrated and stymied by the seemingly unstoppable enemy. Arthas took increasingly extreme steps to conquer them, and his comrades warned him that he was losing his hold on his humanity. Arthas's fear and resolve proved to be his ultimate undoing. He tracked the plague's source to Northrend, intending to end its threat forever. Instead, the prince eventually fell prey to the Lich King's (Ner'zhul's) tremendous power when he took up the cursed runeblade, Frostmourne, believing that it would save his people. Though the sword did grant him unfathomable power, it also stole his soul and transformed him into the greatest of the Lich King's death knights.[2] With his soul cast aside and his sanity shattered, Arthas led the Scourge against his own kingdom. He murdered his father, King Terenas, and crushed the realms of Lordaeron, Quel'Thalas and Dalaran under the Lich King's iron heel.[3]

When the Lich King was threatened by the forces of Illidan Stormrage, Arthas traveled to the Frozen Throne of Northrend. He broke the ice surrounding his master so he could don the Lich King's Helm of Domination and merge with him. After taking control of the Scourge as the new Lich King, Arthas challenged the Alliance and the Horde by initiating attacks on their cities. They responded by sending forces to Northrend to wage war against him.

In World of Warcraft, Arthas is a raid boss and the primary antagonist of the Wrath of the Lich King expansion. He was mortally wounded after a band of adventurers led by Tirion Fordring stormed his fortress, Icecrown Citadel, and defeated him in battle. He was succeeded as the Lich King by Bolvar Fordragon.[4]

Heroes of the Storm[edit]

Arthas appears as a playable character in the crossover game Heroes of the Storm.[5] In the game, Arthas is a warrior hero who performs a tanking role on the battlefield. His aim is to attract the attention of enemy players, as he can withstand a large amount of incoming damage thanks to his necromantic self-healing powers, meanwhile disrupting the enemy team with crowd control abilities.[6] Arthas is proficient against melee physical attackers, slowing their move and attack speed. His playstyle is somewhat limited and predictable due to his lack of mobility, yet he is extremely strong in almost any scenario involving teamwork.[7] One of the two heroic abilities allows him to summon Sindragosa, a mighty frost wyrm, that appears and flies over a portion of the battlefield, slowing and disabling enemies with her frost breath. Arthas Menethil is one of the six Blizzard characters who appear in the Heroes of the Storm cinematic trailer.[8]

Other appearances[edit]

In Hearthstone, Prince Arthas Menethil is an alternate hero for the Paladin class, which can be achieved as a visual alteration for the default paladin hero by defeating the Lich King in the final Knights of the Frozen Throne single-player mission with all nine classes.[9]

Reception[edit]

The character has received mostly positive reception, and is often included on lists involving the most popular Warcraft characters and video game characters as a whole. Empire listed Arthas at No. 25 on their list of "the 50 greatest video game characters", writing "Of all the characters in Warcraft lore, Arthas Menethil is the most tragic."[10] He was also included on "The 10 best video-game characters" list by The Guardian, which stated that "initially the valiant model of a medieval knight, everything changes when Arthas picks up a cursed sword and begins to perpetrate a steadily more sinister series of atrocities (think dead peasants), culminating in killing his own father. The character really came into his own in the mighty World of Warcraft, over which his twisted spirit presided for five years."[11]

Matthew Rossi of Engadget listed the Lich King at No. 4 on his list of the "Top 10 magnificent bastards of Warcraft", since he "successfully molded Arthas into the perfect death knight ... Arthas went from an earnest young prince and paladin trying desperately to save his people to a cackling villain who betrayed them, and it was more Arthas' doing than the Lich King's that Illidan was defeated."[12] He also wrote that "Arthas was useful because he started as a basically good, if somewhat arrogant, young paladin who slowly grew obsessed over time as he witnessed the actions of the Scourge, making mistakes ... and then justifying each mistake as a necessity. By the time he took up Frostmourne and lost his soul, he'd long since eroded it away with expedient choices that were, in fact, monstrous ... Arthas as a death knight and later Arthas as the Lich King showed this tendency to want to justify or prove his actions were the right ones, that anyone would have done what he did."[13] Rossi stated that the lesson of Arthas was "Ultimately, that power corrupts. Power corrupted him, and it will corrupt you, too. That it is inescapable [...] that becoming the Lich King was inevitable, that all kings and princes and people of power ultimately end up slaves to themselves."[14]

Arthas was listed on Complex's list of "25 dead video game characters we wish were still here", noting that "in the same way that Boromir was corrupted in Lord of the Rings, Arthas represents the folly of man, and how easily power can be corrupted. Because of this, we almost want him to survive just to serve as an example that redemption is possible in anyone. If the Lich King had been able to turn around his ways, then there would've been hope for us all."[15] IGN found Arthas to be one of "gaming's most notorious anti-heroes", since "Arthas Menethil began as something of a Disney prince, upholding the Light wherever he saw the need. But with the arrival of the plague of undeath, the Light in Arthas began to waver ... but as is often the case, he wasn't a simple prince-turned-insane-villain. The newly formed Lich King may have been evil, but he was keeping the undead Scourge in check, holding back the flood of the decrepit and the mindless."[16]

Arthas also features in Warcraft-related merchandise, such as Halloween costumes.[17]

References[edit]

^ Jump up to:a b "Rise and Fall of the Lich King: WoW Developer Interview". Retrieved September 9, 2016.

^ Golden, Christie (2009). Arthas: Rise of the Lich King.

^ Blizzard Entertainment (2002). Warcraft III: Reign of Chaos (PC). Blizzard Entertainment. Scene: Arthas' Betrayal.

^ Blizzard Entertainment (2008). World of Warcraft: Wrath of the Lich King (PC). Blizzard Entertainment. Scene: Fall of the Lich King.

^ "Arthas - Heroes of the Storm". us.battle.net. Retrieved 2019-12-21.

^ "Arthas: Non-Compete Hero Guide". Archived from the original on 2015-12-28. Retrieved 2015-07-15.

^ "Heroes of The Storm Heroes: Arthas Guide". 2p.com. Retrieved September 9, 2016.

^ Heroes of the Storm™ Cinematic Trailer, retrieved 2019-12-21

^ Hearthside Chat with Dave Kosak: Knights of the Frozen Throne Missions, retrieved 2019-12-21

^ "The 50 Greatest Video Game Characters". Empire. Retrieved September 9, 2016.

^ "The 10 best video-game characters". The Guardian. 7 August 2010. Retrieved September 9, 2016.

^ "Know Your Lore: Top 10 magnificent bastards of Warcraft, part 2". Engadget. Retrieved September 9, 2016.

^ "Know Your Lore: The role of characters in WoW lore". Engadget. Retrieved September 9, 2016.

^ "Know Your Lore: The Lessons of the Lich King". Engadget. Retrieved September 9, 2016.

^ "25 Dead Video Game Characters We Wish Were Still Here". Complex. Retrieved September 9, 2016.

^ "Gaming's most notorious anti-heroes". IGN. Retrieved September 9, 2016.

^ "Blizzard store now offering full Halloween costumes". Engadget. Retrieved September 9, 2016.

External links[edit]

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olitician who has been serving as General Secretary of the Chinese Communist Party (CCP) and Chairman of the Central Military Commission (CMC) since 2012, and President of the People's Republic of China (PRC) since 2013. Xi has been the paramount leader of China, the most prominent political leader in China, since 2012.

The son of Chinese Communist veteran Xi Zhongxun, he was exiled to rural Yanchuan County as a teenager following his father's purge during the Cultural Revolution, and lived in a Yaodong in the village of Liangjiahe, where he joined the CCP and worked as the party secretary. After studying chemical engineering at Tsinghua University as a "Worker-Peasant-Soldier student", Xi rose through the ranks politically in China's coastal provinces. Xi was Governor of Fujian from 1999 to 2002, before becoming Governor and Party Secretary of neighbouring Zhejiang from 2002 to 2007. Following the dismissal of the Party Secretary of Shanghai, Chen Liangyu, Xi was transferred to replace him for a brief period in 2007. He subsequently joined the Politburo Standing Committee of the CCP and served as first secretary of the Central Secretariat in October 2007. In 2008, he was designated as Hu Jintao's presumed successor as paramount leader; to that end, Xi was appointed Vice President of the People's Republic of China and Vice Chairman of the Central Military Commission. He officially received the title of "leadership core" from the Chinese Communist Party (CCP) in 2016. Xi has also been a member of the 17th, 18th, 19th CCP Politburo Standing Committee since 2007. In 2018, he abolished presidential term limits.

Xi is the first CCP General Secretary born after the establishment of the People's Republic of China. Since assuming power, Xi has introduced far-ranging measures to enforce party discipline and to impose internal unity. His anti-corruption campaign has led to the downfall of prominent incumbent and retired Communist Party officials, including a member of the Politburo Standing Committee. He has also enacted or promoted a more assertive foreign policy, particularly with regard to China–Japan relations, China's claims in the South China Sea, and its advocacy for free trade and globalization. He has sought to expand China's African and Eurasian influence through the Belt and Road Initiative.

Xi has often been described as a dictator or an authoritarian leader by political and academic observers,[9] citing an increase of censorship and mass surveillance, a deterioration in human rights including the internment of Uyghur Muslims in Xinjiang, the cult of personality developing around him,[10] and the removal of term limits for the leadership under his tenure.[a] Xi's political thoughts have been incorporated into the party and national constitutions.[25][26][27] As the central figure of the fifth generation of leadership of the People's Republic, Xi has significantly centralised institutional power by taking on a wide range of leadership positions, including chairing the newly formed National Security Commission, as well as new steering committees on economic and social reforms, military restructuring and modernization, and the Internet.[28]

On 11 November 2021, China's Communist Party declared Xi's ideology the "essence of Chinese culture".[29] This is the third fundamental resolution of the Chinese Communist Party since its inception. The first resolution was adopted in 1945 to increase and ratify the power of Mao Zedong. The decision to issue one under Xi symbolically raises him to the same level of prestige as Mao.[29]

Contents

1Early life and education

2Rise to power

3Politburo Standing Committee member3.1Trips as Vice President

3.2Mexico commentary incident

3.3Disappearance

4Leadership4.1Accession to top posts

4.2Anti-corruption campaign

4.3Censorship

4.4Consolidation of power

4.5Economic policy

4.6Reforms

4.7Foreign policy

4.8Human rights

4.9COVID-19 pandemic

4.10Environmental policy

5Political positions5.1Chinese Dream

5.2Cultural revival

5.3Xi Jinping Thought

5.4Role of the Communist Party

5.5Hong Kong and Taiwan

6Personal life6.1Family

6.2Personality

6.3Public image

7Honours

8Works

9Notes

10References10.1Citations

10.2Works cited

11Further reading

12External links

Early life and education

Xi Jinping was born in Beijing on 15 June 1953, the second son of Xi Zhongxun and his wife Qi Xin. After the founding of the People's Republic of China in 1949 by Mao Zedong, Xi's father held a series of posts, including Party propaganda chief, vice-premier, and Vice Chairperson of the National People's Congress.[30] Xi had two older sisters, Qiaoqiao, born in 1949 and An'an (安安; Ān'ān), born in 1952.[31][32] Xi's father was from Fuping County, Shaanxi, and Xi could further trace his patrilineal descent from Xiying in Dengzhou, Henan.[33]

Xi went to the Beijing No. 25 School,[34] and then Beijing Bayi School,[35][36] in the 1960s. He became friends with Liu He, who attended Beijing No. 101 School in the same district, who later became China's vice-premier and a close advisor to Xi after he became China's paramount leader.[37][38] In 1963, when he was age 10, his father was purged from the Party and sent to work in a factory in Luoyang, Henan.[39] In May 1966, the Cultural Revolution cut short Xi's secondary education when all secondary classes were halted for students to criticise and fight their teachers. Student militants ransacked the Xi family home and one of Xi's sisters, Xi Heping, committed suicide from the pressure.[40] Later, his mother was forced to publicly denounce his father, as he was paraded before a crowd as an enemy of the revolution. His father was later thrown into prison in 1968 when Xi was aged 15. Without the protection of his father, Xi was sent to work in Liangjiahe Village, Wen'anyi, Yanchuan County, Yan'an, Shaanxi, in 1969 in Mao Zedong's Down to the Countryside Movement.[41] He worked as the party secretary of Liangjiahe, where he lived in a cave house.[42] After a few months, unable to stand rural life, he ran away to Beijing. He was arrested during a crackdown on deserters from the countryside and sent to a work camp to dig ditches, but later returned to the village, spending a total of seven years there.[43][44]

The misfortunes and suffering of his family in his early years hardened Xi's view of politics. During an interview in 2000, he said, "People who have little contact with power, who are far from it, always see these things as mysterious and novel. But what I see is not just the superficial things: the power, the flowers, the glory, the applause. I see the bullpens and how people can blow hot and cold. I understand politics on a deeper level." The bullpens was a reference to Red Guards' detention houses during the Cultural Revolution.[45]

After being rejected seven times, Xi joined the Communist Youth League of China in 1971 by befriending a local official.[46] He reunited with his father in 1972, because of a family reunion ordered by Premier Zhou Enlai.[40] From 1973, he applied to join the Chinese Communist Party ten times and was finally accepted on his tenth attempt in 1974.[47][48]

From 1975 to 1979, Xi studied chemical engineering at Beijing's Tsinghua University as a "Worker-Peasant-Soldier student". The engineering majors there spent about 15 percent of their time studying Marxism–Leninism–Mao Zedong thought and 5 percent of their time doing farm work and "learning from the People's Liberation Army".[49]

Rise to power

From 1979 to 1982, Xi served as secretary for his father's former subordinate Geng Biao, the then vice premier and secretary-general of the Central Military Commission. This gained Xi some military background.[46] In 1985, as part of a Chinese delegation to study U.S. agriculture, he stayed in the home of an American family in the town of Muscatine, Iowa. This trip, and his two-week stay with a U.S. family, is said to have had a lasting impression upon him and his views on the United States.[50]

In 1982, he was sent to Zhengding County in Hebei as deputy party secretary of Zhengding County. He was promoted in 1983 to secretary, becoming the top official of the county.[51] Xi subsequently served in four provinces during his regional political career: Hebei (1982–1985), Fujian (1985–2002), Zhejiang (2002–2007), and Shanghai (2007).[52] Xi held posts in the Fuzhou Municipal Party Committee and became the president of the Party School in Fuzhou in 1990. In 1997, he was named an alternate member of the 15th Central Committee of the CCP. However, of the 151 alternate members of the Central Committee elected at the 15th Party Congress, Xi received the lowest number of votes in favour, placing him last in the rankings of members, ostensibly due to his status as a princeling.[note 2][53]

From 1998 to 2002, Xi studied Marxist theory and ideological education in Tsinghua University,[54] graduating from there with a doctorate in law and ideology in 2002.[55] In 1999, he was promoted to the office of Vice Governor of Fujian, then he became governor a year later. In Fujian, Xi made efforts to attract investment from Taiwan and to strengthen the private sector of the provincial economy.[56] In February 2000, he and then-provincial Party Secretary Chen Mingyi were called before the top members of the Party Central Politburo Standing Committee of the CCP – General Secretary Jiang Zemin, Premier Zhu Rongji, Vice-President Hu Jintao and Discipline Inspection Secretary Wei Jianxing – to explain aspects of the Yuanhua scandal.[57]

In 2002, Xi left Fujian and took up leading political positions in neighbouring Zhejiang. He eventually took over as provincial Party Committee Secretary after several months as acting governor, occupying a top provincial office for the first time in his career. In 2002, he was elected a full member of the 16th Central Committee, marking his ascension to the national stage. While in Zhejiang, Xi presided over reported growth rates averaging 14% per year.[58] His career in Zhejiang was marked by a tough and straightforward stance against corrupt officials. This earned him a name in the national media and drew the attention of China's top leaders.[59]

Following the dismissal of Shanghai Party secretary Chen Liangyu in September 2006 due to a social security fund scandal, Xi was transferred to Shanghai in March 2007 where he was the party secretary there for seven months.[60][61] In Shanghai, Xi avoided controversy and was known for strictly observing party discipline. For example, Shanghai administrators attempted to earn favour with him by arranging a special train to shuttle him between Shanghai and Hangzhou for him to complete handing off his work to his successor as Zhejiang party secretary Zhao Hongzhu. However, Xi reportedly refused to take the train, citing a loosely enforced party regulation which stipulated that special trains can only be reserved for "national leaders".[62] While in Shanghai, he worked on preserving unity of the local party organisation. He pledged there would be no 'purges' during his administration, despite the fact many local officials were thought to have been implicated in the Chen Liangyu corruption scandal.[63] On most issues Xi largely echoed the line of the central leadership.[64]

Politburo Standing Committee member

Xi Jinping greeting U.S. President George W. Bush in August 2008.

Xi Jinping with Russian President Dmitry Medvedev on 28 September 2010.

Xi was appointed to the nine-man Politburo Standing Committee of the CCP at the 17th Party Congress in October 2007. He was ranked above Li Keqiang, an indication that he was going to succeed Hu Jintao as China's next leader. In addition, Xi also held the first secretary of the Communist Party's Central Secretariat. This assessment was further supported at the 11th National People's Congress in March 2008, when Xi was elected as vice-president of the People's Republic of China.[65][better source needed] Following his elevation, Xi has held a broad range of portfolios. He was put in charge of the comprehensive preparations for the 2008 Summer Olympics in Beijing, as well as being the central government's leading figure in Hong Kong and Macau affairs. In addition, he also became the new president of the Central Party School of the CCP, the cadre-training and ideological education wing of the Communist Party. In the wake of the 2008 Sichuan earthquake, Xi visited disaster areas in Shaanxi and Gansu. He made his first foreign trip as vice president to North Korea, Mongolia, Saudi Arabia, Qatar and Yemen from 17 to 25 June 2008.[66] After the Olympics, Xi was assigned the post of committee chair for the preparations of the 60th Anniversary Celebrations of the founding of the People's Republic of China. He was also reportedly at the helm of a top-level Communist Party committee dubbed the 6521 Project, which was charged with ensuring social stability during a series of politically sensitive anniversaries in 2009.[67]

Xi's position as the apparent successor to become the paramount leader was threatened with the rapid rise of Bo Xilai, the party secretary of Chongqing at the time. Bo was expected to join the Politburo Standing Committee at the 18th Party Congress, with the possibility of creating a counterweight to Xi, or even replacing him.[68] Bo's policies in Chongqing inspired imitations throughout China and received praise from Xi himself during Xi's visit to Chongqing in 2010. Records of praises from Xi were later erased after he became paramount leader. Xi's position as successor was secured with Bo's downfall after the Wang Lijun incident.[69]

Xi is considered one of the most successful members of the Crown Prince Party, a quasi-clique of politicians who are descendants of early Chinese Communist revolutionaries. Former prime minister of Singapore, Lee Kuan Yew, when asked about Xi, said he felt he was "a thoughtful man who has gone through many trials and tribulations".[70] Lee also commented: "I would put him in the Nelson Mandela class of persons. A person with enormous emotional stability who does not allow his personal misfortunes or sufferings affect his judgment. In other words, he is impressive".[71] Former U.S. Treasury Secretary Henry Paulson described Xi as "the kind of guy who knows how to get things over the goal line".[72] Australian Prime Minister Kevin Rudd said that Xi "has sufficient reformist, party and military background to be very much his own man".[73]

Trips as Vice President

In February 2009, in his capacity as vice-president, Xi Jinping embarked on a tour of Latin America, visiting Mexico,[74] Jamaica,[75] Colombia,[76] Venezuela,[77] and Brazil[78] to promote Chinese ties in the region and boost the country's reputation in the wake of the global financial crisis. He also visited Valletta, Malta, before returning to China.[79]

Mexico commentary incident

On 11 February 2009, while visiting Mexico, Xi spoke in front of a group of overseas Chinese and explained China's contributions during the international financial crisis, saying that it was "the greatest contribution towards the whole of human race, made by China, to prevent its 1.3 billion people from hunger".[note 3] He went on to remark: "There are some bored foreigners, with full stomachs, who have nothing better to do than point fingers at us. First, China doesn't export revolution; second, China doesn't export hunger and poverty; third, China doesn't come and cause you headaches. What more is there to be said?"[note 4][80] The story was reported on some local television stations. The news led to a flood of discussions on Chinese Internet forums and it was reported that the Chinese Ministry of Foreign Affairs was caught off-guard by Xi's remarks, as the actual video was shot by some accompanying Hong Kong reporters and broadcast on Hong Kong TV, which then turned up on various Internet video websites.[81]

In the European Union, Xi visited Belgium, Germany, Bulgaria, Hungary and Romania from 7 to 21 October 2009.[82] He visited Japan, South Korea, Cambodia, and Myanmar on his Asian trip from 14 to 22 December 2009.[83] He later visited the United States, Ireland and Turkey in February 2012. This visit included meeting with then U.S. President Barack Obama at the White House[84] and then Vice President Joe Biden; and stops in California and Iowa, where he met with the family which previously hosted him during his 1985 tour as a Hebei provincial official.[85]

Disappearance

A few months before his ascendancy to the party leadership, Xi disappeared from official media coverage for several weeks beginning on 1 September 2012. On 4 September, he cancelled a meeting with U.S. Secretary of State Hillary Clinton, and later also cancelled meetings with Singapore's Prime Minister Lee Hsien Loong and a top Russian official. It was said that Xi effectively "went on strike" in preparation for the power transition in order to install political allies in key roles.[46] The Washington Post reported from a single source that Xi may have been injured in an altercation during a meeting of the "red second generation" which turned violent.[86]

Leadership

Main article: Xi Jinping Administration

Accession to top posts

See also: Generations of Chinese leadership and Succession of power in China

On 15 November 2012, Xi was elected to the posts of general secretary of the Communist Party and chairman of the CCP Central Military Commission by the 18th Central Committee of the CCP. This made him, informally, the paramount leader and the first to be born after the founding of the People's Republic of China. The following day Xi led the new line-up of the Politburo Standing Committee onto the stage in their first public appearance.[87] The new Standing Committee reduced its number of seats from nine to seven, with only Xi himself and Li Keqiang retaining their seats from the previous Standing Committee; the remaining members were new.[88][89][90] In a marked departure from the common practice of Chinese leaders, Xi's first speech as general secretary was plainly worded and did not include any political slogans or mention of his predecessors.[91] Xi mentioned the aspirations of the average person, remarking, "Our people ... expect better education, more stable jobs, better income, more reliable social security, medical care of a higher standard, more comfortable living conditions, and a more beautiful environment." Xi also vowed to tackle corruption at the highest levels, alluding that it would threaten the Party's survival; he was reticent about far-reaching economic reforms.[92]

In December 2012, Xi visited Guangdong in his first trip outside Beijing since taking the Party leadership. The overarching theme of the trip was to call for further economic reform and a strengthened military. Xi visited the statue of Deng Xiaoping and his trip was described as following in the footsteps of Deng's own southern trip in 1992, which provided the impetus for further economic reforms in China after conservative party leaders stalled many of Deng's reforms in the aftermath of the Tiananmen Square protests of 1989. On his trip, Xi consistently alluded to his signature slogan the "Chinese Dream". "This dream can be said to be the dream of a strong nation. And for the military, it is a dream of a strong military", Xi told sailors.[93] Xi's trip was significant in that he departed from the established convention of Chinese leaders' travel routines in multiple ways. Rather than dining out, Xi and his entourage ate regular hotel buffet. He travelled in a large van with his colleagues rather than a fleet of limousines, and did not restrict traffic on the parts of the highway he travelled.[94]

Xi was elected President of the People's Republic of China on 14 March 2013, in a confirmation vote by the 12th National People's Congress in Beijing. He received 2,952 for, one vote against, and three abstentions.[87] He replaced Hu Jintao, who retired after serving two terms.[95] In his new capacity as president, on 16 March 2013 Xi expressed support for non-interference in China–Sri Lanka relations amid a United Nations Security Council vote to condemn that country over government abuses during the Sri Lankan Civil War.[96] On 17 March, Xi and his new ministers arranged a meeting with the chief executive of Hong Kong, CY Leung, confirming his support for Leung.[97] Within hours of his election, Xi discussed cyber security and North Korea with U.S. President Barack Obama over the phone. Obama announced the visits of treasury and state secretaries Jacob Lew and John F. Kerry to China the following week.[98]

Anti-corruption campaign

Main article: Anti-corruption campaign under Xi Jinping

Xi vowed to crack down on corruption almost immediately after he ascended to power at the 18th Party Congress. In his inaugural speech as general secretary, Xi mentioned that fighting corruption was one of the toughest challenges for the party.[99] A few months into his term, Xi outlined the "eight-point guide", listing rules intended to curb corruption and waste during official party business; it aimed at stricter discipline on the conduct of party officials. Xi also vowed to root out "tigers and flies", that is, high-ranking officials and ordinary party functionaries.[100]

During the first three years of Xi's term, he initiated cases against former Central Military Commission vice-chairmen Xu Caihou and Guo Boxiong, former Politburo Standing Committee member and security chief Zhou Yongkang and former Hu Jintao chief aide Ling Jihua.[101] Along with new disciplinary chief Wang Qishan, Xi's administration spearheaded the formation of "centrally-dispatched inspection teams" (中央巡视组). These were essentially cross-jurisdictional squads of officials whose main task was to gain more in-depth understanding of the operations of provincial and local party organizations, and in the process, also enforce party discipline mandated by Beijing. Many of the work teams also had the effect of identifying and initiating investigations of high-ranking officials. Over one hundred provincial-ministerial level officials were implicated during a massive nationwide anti-corruption campaign. These included former and current regional officials (Su Rong, Bai Enpei, Wan Qingliang), leading figures of state-owned enterprises and central government organs (Song Lin, Liu Tienan), and highly ranked generals in the military (Gu Junshan). In June 2014, the Shanxi provincial political establishment was decimated, with four officials dismissed within a week from the provincial party organization's top ranks. Within the first two years of the campaign alone, over 200,000 low-ranking officials received warnings, fines, and demotions.[102]

The campaign has led to the downfall of prominent incumbent and retired Communist Party officials, including members of the Politburo Standing Committee.[103] Xi's anti-corruption campaign is seen by critics[who?] as a political purge on a scale not seen since Chairman Mao, with the aim of removing potential opponents and consolidating power. Xi's establishment of a new anti-corruption agency, the National Supervision Commission, that is ranked higher than the supreme court, has been described by Amnesty International's East Asia director as a "systemic threat to human rights" which "places tens of millions of people at the mercy of a secretive and virtually unaccountable system that is above the law."[104][105]

Censorship

See also: Censorship in China

"Document No. 9" is a confidential internal document widely circulated within the Chinese Communist Party in 2013 by the party's General Office.[106][107] It was first published in July 2012.[108] The document warns of seven dangerous Western values:

Constitutional democracy, which includes such tenets as multi-party systems, the separation of powers, general elections, and judicial independence;[109]

Universal values, a notion contrary to Maoist doctrine, whereby the Western value system transcends nation in class, and applies to China.[110][111]

Civil society, the notion that individual rights are paramount, rather than the collective rights established by the Party;

Pro-market neoliberalism, referring to libertarian economic values and globalization;[112]

Media independence, as Xi was especially hostile to Western ideas of journalism and the notion of a press that could criticize government and Party policies[113][better source needed]

Historical nihilism; and

Questioning the nature of Chinese style socialism.[114]

Coverage of these topics in educational materials is forbidden.[115] Although it predates Xi Jinping's formal rise to the top party and state posts, the release of this internal document, which has introduced new topics that were previously not "off-limits," was seen as Xi's recognition of the "sacrosanct" nature of Communist Party rule over China.[114]

Internet censorship

See also: Internet censorship in China

Since Xi became the CCP General Secretary, internet censorship in China has been significantly stepped up.[116][117] Chairing the 2018 China Cyberspace Governance Conference on 20 and 21 April 2018, Xi committed to "fiercely crack down on criminal offenses including hacking, telecom fraud, and violation of citizens' privacy."[118] His administration has also overseen more Internet restrictions imposed in China, and is described as being "stricter across the board" on speech than previous administrations.[119] Xi has taken a very strong stand to control internet usage inside China, including Google and Facebook,[120] advocating Internet censorship in the country as the concept of "internet sovereignty."[121][122] The censorship of Wikipedia has also been stringent; as of April 2019, all versions of Wikipedia have been blocked in China.[123] Likewise, the situation for users of Weibo has been described as a change from fearing that individual posts would be deleted, or at worst one's account, to fear of arrest.[124] A law enacted in September 2013 authorized a three-year prison term for bloggers who shared more than 500 times any content considered "defamatory."[125] The State Internet Information Department summoned a group of influential bloggers to a seminar instructing them to avoid writing about politics, the Communist Party, or making statements contradicting official narratives. Many bloggers stopped writing about controversial topics, and Weibo went into decline, with much of its readership shifting to WeChat users speaking to very limited social circles.[125] In 2017, telecommunications carriers in China were instructed by the government to block individuals' use of Virtual Private Networks (VPNs) by February 2018.[126]

Winnie the Pooh caricature and censorship

Meme comparing Winnie the Pooh and Tigger to Xi Jinping and Barack Obama, respectively.

Comparisons between Xi and the Disney character Winnie the Pooh are censored on Chinese internet following the spread of an internet meme in which photographs of Xi were compared to the bear.[127] The first heavily censored viral meme can be traced back to the official visit to the United States in 2013 during which Xi was photographed by a Reuters photographer walking with then-US President Barack Obama in Sunnylands, California. A blog post where the photograph was juxtaposed with the cartoon depiction went viral,[128][129][130] but Chinese censors rapidly deleted it.[131] When Shinzo Abe met Xi the following year, a photograph of the meeting, again juxtaposed to a cartoon, went viral.[128][129] When Xi Jinping inspected troops through his limousine's sunroof, a popular meme was created with Winnie the Pooh in a toy car. The widely circulated image became the most censored picture of the year.[128]

In 2018, the Winnie the Pooh film Christopher Robin was denied a Chinese release,[130][132] following an incident where Chinese authorities censored a nine-year-old for comments about Xi's weight.[133] After the 2020–2021 China–India skirmishes, Indians used depictions of Winnie the Pooh to mock Xi Jinping. The Twitter hashtag #WinniethePooh was used for tweets critical of China's actions.[134]

Consolidation of power

Portrait of Xi in Beijing, September 2015

Political observers have called Xi the most powerful Chinese leader since Chairman Mao Zedong, especially since the ending of presidential two-term limits in 2018.[135][136][137][138] Xi has notably departed from the collective leadership practices of his post-Mao predecessors. He has centralised his power and created working groups with himself at the head to subvert government bureaucracy, making himself become the unmistakable central figure of the new administration.[139] Beginning in 2013, the party under Xi has created a series of new "Central Leading Groups"; supra-ministerial steering committees, designed to bypass existing institutions when making decisions, and ostensibly make policy-making a more efficient process. The most notable new body is the Central Leading Group for Comprehensively Deepening Reforms. It has broad jurisdiction over economic restructuring and social reforms, and is said to have displaced some of the power previously held by the State Council and its premier.[140] Xi also became the leader of the Central Leading Group for Internet Security and Informatization, in charge of cyber-security and Internet policy. The Third Plenum held in 2013 also saw the creation of the National Security Commission of the CCP, another body chaired by Xi which commentators have said would help Xi consolidate over national security affairs.[141][142] In the opinion of at least one political scientist, Xi "has surrounded himself with cadres he met while stationed on the coast, Fujian and Shanghai and in Zhejiang."[143] Control of Beijing is seen as crucial to Chinese leaders; Xi has selected Cai Qi, one of the cadres mentioned above, to manage the capital.[144]

Cult of personality

Holographic portraits of Mao Zedong and Xi Jinping in a shop in China

Main article: Xi Jinping's cult of personality

Xi has had a cult of personality constructed around himself since entering office[26][27] with books, cartoons, pop songs and dance routines honouring his rule.[145] Following Xi's ascension to the leadership core of the CCP, he has been referred to as Xi Dada (Uncle or Papa Xi).[145][146] The village of Liangjiahe, where Xi was sent to work, has become a "modern-day shrine" decorated with Communist propaganda and murals extolling the formative years of his life.[147]

The party's Politburo named Xi Jinping lingxiu), a reverent term for "leader" and a title previously only given to Chiang Kai-shek, Mao Zedong and his immediate successor Hua Guofeng.[148][149][150] He is also sometimes called the "Great Helmsman" (大舵手), and in July 2018 Li Zhanshu, the Chairman of the Standing Committee of the National People's Congress, referred to Xi as the "eternal core" of the party.[151] On 25 December 2019, the politburo officially named Xi as "People's Leader" (rénmín lǐngxiù), a title only Mao had held previously.[152]

Removal of term limits

In March 2018, the party-controlled National People's Congress passed a set of constitutional amendments including removal of term limits for the president and vice president, the creation of a National Supervisory Commission, as well as enhancing the central role of the Communist Party.[153][154] On 17 March 2018, the Chinese legislature reappointed Xi as president, now without term limits; Wang Qishan was appointed vice president.[155][156] The following day, Li Keqiang was reappointed premier and longtime allies of Xi, Xu Qiliang and Zhang Youxia, were voted in as vice-chairmen of the state military commission.[157] Foreign minister Wang Yi was promoted to state councillor and General Wei Fenghe was named defence minister.[158]

According to the Financial Times, Xi expressed his views of constitutional amendment at meetings with Chinese officials and foreign dignitaries. Xi explained the decision in terms of needing to align two more powerful posts—General Secretary of the Communist Party and Chairman of the Central Military Commission (CMC)—which have no term limits. However, Xi did not say whether he intended to serve as party general secretary, CMC chairman and state president, for three or more terms.[159]

Economic policy

Xi has increased state control over China's economy, voicing support for China's state-owned enterprises (SOEs),[160] while also supporting the country's private sector.[161] He has increased the role of the Central Financial and Economic Affairs Commission at the expense of the State Council.[162] His administration made it easier for banks to issue mortgages, increased foreign participation in the bond market, and increased country's currency renminbi's global role, helping it to join IMF's basket of special drawing right.[163] In the 40th anniversary of the launching of Chinese economic reforms in 2018, he has promised to continue reforms but has warned that nobody "can dictate to the Chinese people".[164] Since the outbreak of the China-United States trade war in 2018, Xi has also revived calls for "self-reliance", especially on the matters of technology.[165]

Following a speech by Jack Ma in 2020 where he said that Chinese banks had a "pawnshop mentality" and called out government regulation. Xi was said to have been furious over it and made the decision to halt Ant Group's IPO, leading to a crackdown on Chinese big tech.[166][167] In December 2020, Xi called efforts to increase anti-monopoly rules against online platforms one of the most important goals of 2021.[168] In March 2021, Xi called for the acceleration of the big tech crackdown.[169][170]

Reforms

Agenda announcement

In November 2013, at the conclusion of the Third Plenum of the 18th Central Committee, the Communist Party delivered a far-reaching reform agenda that alluded to changes in both economic and social policy. Xi signaled at the plenum that he was consolidating control of the massive internal security organization that was formerly the domain of Zhou Yongkang.[171] A new National Security Commission was formed with Xi at its helm. The Central Leading Group for Comprehensively Deepening Reforms—another ad hoc policy coordination body led by Xi—was also formed to oversee the implementation of the reform agenda.[172][better source needed] Termed "comprehensive deepening reforms" (àn shēnhuà gǎigé), they were said to be the most significant since Deng Xiaoping's 1992 "Southern Tour". In the economic realm, the plenum announced that "market forces" would begin to play a "decisive" role in allocating resources.[171] This meant that the state would gradually reduce its involvement in the distribution of capital, and restructure state-owned enterprises to allow further competition, potentially by attracting foreign and private sector players in industries that were previously highly regulated. This policy aimed to address the bloated state sector that had unduly profited from an earlier round of re-structuring by purchasing assets at below-market prices, assets which were no longer being used productively. The plenum also resolved to abolish the laogai system of "re-education through labour" which was largely seen as a blot on China's human rights record. The system has faced significant criticism for years from domestic critics and foreign observers.[171] The one-child policy was also abolished, resulting in a shift to a two-child policy from 1 January 2016.[173]

Legal reforms

The party under Xi announced a raft of legal reforms at the Fourth Plenum held in the fall 2014, and he called for "Chinese socialistic rule of law" immediately afterwards. The party aimed to reform the legal system which had been perceived as ineffective at delivering justice and affected by corruption, local government interference and lack of constitutional oversight. The plenum, while emphasizing the absolute leadership of the party, also called for a greater role of the constitution in the affairs of state and a strengthening of the role of the National People's Congress Standing Committee in interpreting the constitution.[174] It also called for more transparency in legal proceedings, more involvement of ordinary citizens in the legislative process, and an overall "professionalization" of the legal workforce. The party also planned to institute cross-jurisdictional circuit legal tribunals as well as giving provinces consolidated administrative oversight over lower level legal resources, which is intended to reduce local government involvement in legal proceedings.[175]

Xi has overseen significant reforms of the Central Commission for Discipline Inspection (CCDI), CCP's highest internal control institution.[176] He and CCDI Secretary Wang Qishan further institutionalised CCDI's independence from the day-to-day operations of the CCP, improving its ability to function as a bona fide control body.[176]

Military reforms

See also: Modernization of the People's Liberation Army and 2015 People's Republic of China military reform

Since taking power in 2012, Xi has started a massive overhaul of the People's Liberation Army.[177] Xi has been active in his participation in military affairs, taking a direct hands-on approach to military reform. In addition to being the Chairman of the Central Military Commission, and the leader of the Central Leading Group for Military Reform founded in 2014 to oversee comprehensive military reforms, Xi has delivered numerous high-profile pronouncements vowing to clean up malfeasance and complacency in the military, aiming to build a more effective fighting force. In addition, Xi held the "New Gutian Conference" in 2014, gathering China's top military officers, re-emphasizing the principle of "the party has absolute control over the army" first established by Mao at the 1929 Gutian Conference.[178]

Xi has warned against the depoliticization of the PLA from the Communist Party, warning that it would lead to a collapse similar to that of the Soviet Union.[179][180] He said that "in the USSR, where the military was depoliticized, separated from the party and nationalized, the party was disarmed. When the Soviet Union came to crisis point, a big party was gone just like that. Proportionally, the Soviet Communist Party had more members than we do, but nobody was man enough to stand up and resist."[180]

Xi announced a reduction of 300,000 troops from the PLA in 2015, bringing its size to 2 million troops. Xi described this as a gesture of peace, while analysts have said that the cut was done to reduce costs as well as part of PLA's modernization.[181] On 2016, he reduced the number of theater commands of the PLA from seven to five.[182] He has also abolished the four autonomous general departments of the PLA, replacing them with 15 agencies directly reporting to the Central Military Commission.[177] Two new branches of the PLA were created under his reforms, the Strategic Support Force[183] and the Joint Logistics Support Force.[184]

On 21 April 2016, Xi was named commander-in-chief of the country's new Joint Operations Command Center of the People's Liberation Army by Xinhua News Agency and the broadcaster China Central Television.[185][186] Some analysts interpreted this move as an attempt to display strength and strong leadership and as being more "political than military".[187] According to Ni Lexiong, a military affairs expert, Xi "not only controls the military but also does it in an absolute manner, and that in wartime, he is ready to command personally".[188] According to a University of California, San Diego expert on Chinese military, Xi "has been able to take political control of the military to an extent that exceeds what Mao and Deng have done".[189]

2020–2021 reform spree

Main article: 2020-2021 Xi Jinping Administration reform spree

In late 2020,[190] the Chinese Communist Party and various Chinese regulatory bodies,[191] under Xi, began a regulatory spree, strengthening regulations, issuing fines,[192] and introducing or modifying laws. Though mostly targeted at disrupting the growth of monopolistic technology companies, the government also introduced other reforms with implications for large swathes of the economy and life in China. Actions taken include the implementation of restrictions on for-profit tutoring and education companies,[193] the refinement of existing rules for limits on minors playing online video games, and the introduction of new antitrust rules.[194] The stated goals of these reforms has been, among others, "common prosperity".[195]

Foreign policy

Main article: Foreign policy of Xi Jinping

Xi giving a speech at the U.S. Department of State in 2012, with then Secretary of State Hillary Clinton and then Vice-President Joe Biden in the background. Seated in the front row is former Secretary of State Henry Kissinger.

A Chinese nationalist,[196] Xi has reportedly taken a hard-line on security issues as well as foreign affairs, projecting a more nationalistic and assertive China on the world stage.[196] His political program calls for a China more united and confident of its own value system and political structure.[197]

Under Xi, China has also taken a more critical stance on North Korea, while improving relationships with South Korea.[198] China–Japan relations have soured under Xi's administration; the most thorny issue between the two countries remains the dispute over the Senkaku islands, which China calls Diaoyu. In response to Japan's continued robust stance on the issue, China declared an Air Defense Identification Zone in November 2013.[199]

Xi has called China–United States relations in the contemporary world a "new type of great-power relations", a phrase the Obama administration had been reluctant to embrace.[200] Under his administration the Strategic and Economic Dialogue that began under Hu Jintao has continued. On China–U.S. relations, Xi said, "If [China and the United States] are in confrontation, it would surely spell disaster for both countries".[201] The U.S. has been critical of Chinese actions in the South China Sea.[200] In 2014, Chinese hackers compromised the computer system of the U.S. Office of Personnel Management,[202] resulting in the theft of approximately 22 million personnel records handled by the office.[203]

Xi has cultivated stronger relations with Russia, particularly in the wake of the Ukraine crisis of 2014. He seems to have developed a strong personal relationship with President Vladimir Putin. Both are viewed as strong leaders with a nationalist orientation who are not afraid to assert themselves against Western interests.[204] Xi attended the opening ceremonies of the 2014 Winter Olympics in Sochi. Under Xi, China signed a $400 billion gas deal with Russia; China has also become Russia's largest trading partner.[204]

BRICS leaders Vladimir Putin, Narendra Modi, Dilma Rousseff, Xi Jinping and Jacob Zuma at the G20 summit in Brisbane, Australia, 15 November 2014

Xi has also indirectly spoken out critically on the U.S. "strategic pivot" to Asia.[205] Addressing a regional conference in Shanghai on 21 May 2014, he called on Asian countries to unite and forge a way together, rather than get involved with third party powers, seen as a reference to the United States. "Matters in Asia ultimately must be taken care of by Asians. Asia's problems ultimately must be resolved by Asians and Asia's security ultimately must be protected by Asians", he told the conference.[206] In November 2014, in a major policy address, Xi called for a decrease in the use of force, preferring dialogue and consultation to solve the current issues plaguing the relationship between China and its South East Asian neighbors.[207]

Xi with the first lady during the Moscow Victory Day Parade on 9 May 2015

In April 2015, new satellite imagery revealed that China was rapidly constructing an airfield on Fiery Cross Reef in the Spratly Islands of the South China Sea.[208] In May 2015, U.S. Secretary of Defense Ash Carter warned the government of Xi Jinping to halt its rapid island-building in disputed territory in the South China Sea.[209] In spite of what seemed to be a tumultuous start to Xi Jinping's leadership vis-à-vis the United-States, on 13 May 2017 Xi said at the Belt and Road Forum in Beijing: "We should foster a new type of international relations featuring 'win-win cooperation', and we should forge a partnership of dialogue with no confrontation, and a partnership of friendship rather than alliance. All countries should respect each other's sovereignty, dignity and territorial integrity; respect each other's development path and its social systems, and respect each other's core interests and major concerns... What we hope to create is a big family of harmonious coexistence."[210]

Xi with Iran's Supreme Leader Ali Khamenei, 23 January 2016

Starting in 2017, China's relationship with South Korea soured over the THAAD purchase of the latter[211] while China's relations with North Korea increased because of meetings between Xi and North Korean leader Kim Jong-un.[212] At the G20 meeting in Japan, Xi called for a "timely easing" of sanctions imposed on North Korea.[213]

Relations with the U.S. soured after Donald Trump became president in 2016.[214] Since 2018, U.S. and China have been engaged in an escalating trade war.[215]

On 4 June 2019, Xi told the Russian news agency TASS that he was "worried" about the current tensions between the U.S. and Iran.[216] He later told his Iranian counterpart Hassan Rouhani during an SCO meeting that China would promote ties with Iran regardless of developments from the Gulf of Oman incident.[217]

U.S. President Donald Trump arrives in China, 8 November 2017

In the 2019, the Pew Research Center made a survey on attitude to Xi Jinping among six-country medians based on Australia, India, Indonesia, Japan, Philippines and South Korea. The survey indicated that a median 29% have confidence in Xi Jinping to do the right thing regarding world affairs, meanwhile a median of 45% have no confidence. These number are almost same with those of North Korean leader Kim Jong Un (23% confidence, 53% no confidence).[218]

Foreign trips as paramount leader

Main article: List of international trips made by Xi Jinping

Xi made his first foreign trip as China's paramount leader to Russia on 22 March 2013, about a week after he assumed the presidency. He met with President Vladimir Putin and the two leaders discussed trade and energy issues. He then went on to Tanzania, South Africa (where he attended the BRICS summit in Durban), and the Republic of the Congo.[219] Xi visited the United States at Sunnylands Estate in California in a 'shirtsleeves summit' with U.S. President Barack Obama in June 2013, although this was not considered a formal state visit.[220] In October 2013 Xi attended the APEC Summit in Bali, Indonesia.

In March 2014 Xi made a trip to Western Europe visiting the Netherlands, where he attended the Nuclear Security Summit in The Hague, followed by visits to France, Germany and Belgium.[221][better source needed] He made a state visit to South Korea on 4 July 2014 and met with South Korean President Park Geun-hye.[222] Between 14 and 23 July, Xi attended the BRICS leaders' summit in Brazil and visited Argentina, Venezuela, and Cuba.[223]

Xi in an official visit to Warsaw, where he and Poland's President Andrzej Duda signed a declaration on strategic partnership

Xi went on an official state visit to India and met with Indian Prime Minister Narendra Modi in September 2014; he visited New Delhi and also went to Modi's hometown in the state of Gujarat.[224] He went on a state visit to Australia and met with Prime Minister Tony Abbott in November 2014,[225] followed by a visit to the island nation of Fiji.[226] Xi visited Pakistan in April 2015, signing a series of infrastructure deals worth $45 billion related to the China–Pakistan Economic Corridor. During his visit, Pakistan's highest civilian award, the Nishan-e-Pakistan, was conferred upon him.[227] He then headed to Jakarta and Bandung, Indonesia, to attend the Afro-Asian Leaders Summit and the 60th Anniversary events of the Bandung Conference.[228] Xi visited Russia and was the guest-of-honour of Russian President Vladimir Putin at the 2015 Moscow Victory Day Parade to mark the 70th Anniversary of the victory of the allies in Europe. At the parade, Xi and his wife Peng Liyuan sat next to Putin. On the same trip Xi also visited Kazakhstan and met with that country's president Nursultan Nazarbayev, and also met Alexander Lukashenko in Belarus.[229]

Xi, who was on a four-day state visit to the UK, addressed both Houses of Parliament at Westminster, 21 October 2015

In September 2015, Xi made his first state visit to the United States.[230][231][232] In October 2015, he made a state visit to the United Kingdom, the first by a Chinese leader in a decade.[233] This followed a visit to China in March 2015 by the Duke of Cambridge. During the state visit, Xi met Queen Elizabeth II, British Prime Minister David Cameron and other dignitaries. Increased customs, trade and research collaborations between China and the UK were discussed, but more informal events also took place including a visit to Manchester City's football academy.[234]

In March 2016, Xi visited the Czech Republic on his way to United States. In Prague, he met with the Czech president, prime minister and other representatives to promote relations and economic cooperation between the Czech Republic and the People's Republic of China.[235] His visit was met by a considerable number of protests by Czechs.[236]

World leaders assemble for 'family photo' at G20 summit in Hamburg

In January 2017, Xi became the first Chinese paramount leader to plan to attend the World Economic Forum in Davos.[237] On 17 January, Xi addressed the forum in a high-profile keynote, addressing globalization, the global trade agenda, and China's rising place in the world's economy and international governance; he made a series of pledges about China's defense of "economic globalization" and climate change accords.[237][238][239] Premier Li Keqiang attended the forum in 2015 and Vice-President Li Yuanchao did so in 2016. During the three-day state visit to the country in 2017 Xi also visited the World Health Organization, the United Nations and the International Olympic Committee.[239]

On 20 June 2019, Xi Jinping visited Pyongyang, becoming the first Chinese leader to visit North Korea since his predecessor Hu Jintao's visit in 2004.[240] On 27 June, he attended the G20 summit in Osaka, becoming the first Chinese leader to visit Japan since 2010.[241]

Belt and Road Initiative

Main article: Belt and Road Initiative

Countries which signed cooperation documents related to the Belt and Road Initiative

The Belt and Road Initiative (BRI) was unveiled by Xi in September and October 2013 during visits to Kazakhstan and Indonesia,[242] and was thereafter promoted by Premier Li Keqiang during state visits to Asia and Europe. Xi made the announcement for the initiative while in Astana, Kazakhstan, and called it a "golden opportunity".[243][better source needed] BRI has been called Xi's "signature project", involving numerous infrastructure development and investment projects throughout Asia, Europe, Africa, and the Americas.[244] BRI was added to the CCP Constitution at the closing session of the 19th Party Congress on 24 October 2017,[245] further elevating its importance.[246]

Human rights

Main article: Human rights in China

According to the Human Rights Watch, Xi has "started a broad and sustained offensive on human rights" since he became leader in 2012.[247] The HRW also said that repression in China is "at its worst level since the Tiananmen Square massacre."[248] Since taking power, Xi has cracked down on grassroots activism, with hundreds being detained.[249] He presided over the 709 crackdown on 9 July 2015, which saw more than 200 lawyers, legal assistants and human rights activists being detained.[250] His term has seen the arrest and imprisonment of activists such as Xu Zhiyong, as well as numerous others who identified with the New Citizens' Movement. Prominent legal activist Pu Zhiqiang of the Weiquan movement was also arrested and detained.[251]

In 2017, the local government of the Jiangxi province told Christians to replace their pictures of Jesus with Xi Jinping as part of a general campaign on unofficial churches in the country.[252][253][254] According to local social media, officials "transformed them from believing in religion to believing in the party".[252] According to activists, "Xi is waging the most severe systematic suppression of Christianity in the country since religious freedom was written into the Chinese constitution in 1982", and according to pastors and a group that monitors religion in China, has involved "destroying crosses, burning bibles, shutting churches and ordering followers to sign papers renouncing their faith".[255]

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