Probability
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[Mission completion details are as follows: Guide students to complete the "Collatz conjecture".
Students: Vera, Qin Yue, Hardy. Student engagement: 70%. Type of experience: Mathematics.
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The academic value of the Collatz conjecture was actually lowered than the twin prime conjecture.
However, the Collatz conjecture was a lot more difficult to solve than the twin prime conjecture.
Of course, that was before the "Group Structure Method" was invented.
When Lu Zhou was studying the twin prime conjecture, he used a topology large sieve method. He developed the Group Structure Method when he was studying the Polignac's conjecture.