20200219, 18:55  #1 
Mar 2018
1000011110_{2} 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^22 where s is a prime... Infact 2=2^22, 7=3^22 and 359=19^22 Last fiddled with by enzocreti on 20200219 at 19:06 
20200220, 04:00  #2 
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.

20200220, 08:46  #3 
Mar 2018
2·271 Posts 
....
if a prime p has the form 8s+1 or 8s+5
then 10^d*(2^p1)+2^(p1)1 is divisible by 5 
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