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Prove infinitely many prime of the form 6k+5

  1. Nov 25, 2011 #1
    1. The problem statement, all variables and given/known data
    Prove that there are infinitely many prime of the form 6k+5, where k is nonnegative integer.


    2. Relevant equations



    3. The attempt at a solution
    Prove by contradiction. Suppose there are finitely many prime of the form 6k+5. Then
    i get stucked. Anyone can help me ??
     
  2. jcsd
  3. Nov 26, 2011 #2

    Bacle2

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    Well, there isa result that any arithmetic progression an=a0+nr
    with a0 and r relatively prime contains infinitely-many primes. Is that the type of proof you want (adapted to a0=5 and r=6)?
     
  4. Nov 26, 2011 #3

    Dick

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    You got "stucked" before you really got started. Suppose M=p1*p2*...*pk where the p's are your primes. Think about the prime factorization of 3*M+2. Can you show none of the p's are factors? Can you show at least one of the factors must be equal to 5 mod 6?
     
  5. Nov 26, 2011 #4

    Dick

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    That proof is way too hard. There are simpler proofs for special cases. This is one of them.
     
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