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Primary problem III (Posted on 2015-07-03) Difficulty: 3 of 5
Prove that there are infinitely many primes of the form 3n + 1.

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

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Solution Prime answer | Comment 1 of 2
Suppose p1, p2, ..., px are all of the primes of the form 3n+1. Let q=p1*p2*...*px. The number 4q^2+3 cannot be divisible by any of p1, p2, ..., px. However, it can only have factors of the form 3n+1. Therefore, there are infinitely many primes of the form 3n+1.

  Posted by Math Man on 2015-07-03 19:30:19
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