9 Jan
2007
9 Jan
'07
7:45 p.m.
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