[math-fun] CORRECTION Re: Question about primes
MAKE THAT INSTEAD: Is it known whether for each odd prime p there exists at least one odd prime q such that pq + 2 is prime? --Dan
On 1/9/07, Daniel Asimov <dasimov@earthlink.net> wrote:
MAKE THAT INSTEAD:
Is it known whether for each odd prime p there exists at least one odd prime q such that pq + 2 is prime?
--Dan
For grins I looked at twin primes p, q = p + 2, such that pq + 2 is prime. It would seem that there are infinitely many such p. Except for p = 3 and p = 5 all such p appear to be of the form 30k - 1. Probably this is easy to show, but I didn't try. The sequence of k which gives such twin primes starts out 5, 6, 8, 9, 14, 19, 43, 44, 77, 85, 91, 112, 113, 142, 155, ... and is in OEIS as A125251. Jim
On Wednesday 10 January 2007 02:32, James Buddenhagen wrote:
For grins I looked at twin primes p, q = p + 2, such that pq + 2 is prime. It would seem that there are infinitely many such p. Except for p = 3 and p = 5 all such p appear to be of the form 30k - 1. Probably this is easy to show, but I didn't try.
Yup, it's easy. Prime numbers (other than 2,3,5) are 30k + 1,7,11,13,17,19,23,29. p+2 is then prime only for p = 30k + 11,17,29; then p(p+2)+2 is 30k + 25,25,1 respectively, so the last case mod 30 is the only one possible. -- g
participants (3)
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Daniel Asimov -
Gareth McCaughan -
James Buddenhagen