mersenneforum.org Why primes are either of the form 8n+3 or 8n+7
 Register FAQ Search Today's Posts Mark Forums Read

 2020-02-19, 18:55 #1 enzocreti   Mar 2018 10000111102 Posts Why primes are either of the form 8n+3 or 8n+7 2, 3, 7, 19, 67, 79, 359, 2131, 3371, 331259 are the k's (k is prime) such that pg(k) is also prime First I note that the primes have either the form 8n+3 or 8n+7 or 8n+2 (why?) The primes that are not of the form 8n+3, that is 2, 7 and 359 are of the form s^2-2 where s is a prime... Infact 2=2^2-2, 7=3^2-2 and 359=19^2-2 Last fiddled with by enzocreti on 2020-02-19 at 19:06
 2020-02-20, 04:00 #2 jwaltos   3×29×83 Posts One of the best ways to answer this question (without posting) is to try and find the answer in a text book or peer reviewed paper. If you haven't found it after a quick search then you haven't looked hard enough.
 2020-02-20, 08:46 #3 enzocreti   Mar 2018 2·271 Posts .... if a prime p has the form 8s+1 or 8s+5 then 10^d*(2^p-1)+2^(p-1)-1 is divisible by 5

 Similar Threads Thread Thread Starter Forum Replies Last Post sweety439 sweety439 179 2023-08-08 19:54 enzocreti enzocreti 0 2020-02-17 16:28 enzocreti enzocreti 7 2019-05-05 13:19 a1call Miscellaneous Math 6 2018-12-11 03:34 carpetpool carpetpool 3 2017-01-26 01:29

All times are UTC. The time now is 04:21.

Sun Sep 24 04:21:44 UTC 2023 up 11 days, 2:04, 0 users, load averages: 2.24, 2.02, 1.81