|
2020-02-19, 18:55
|
#1 |
|
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 |
|
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 |
|
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 |
|
|
|
 |
| Thread Tools | |
Similar Threads
|
||||
| Thread | Thread Starter | Forum | Replies | Last Post |
| Primes of the form (b±1)*b^n±1 and b^n±(b±1) | sweety439 | sweety439 | 179 | 2023-08-08 19:54 |
| primes of the form (123+4^(9*10^n))/163 | enzocreti | enzocreti | 0 | 2020-02-17 16:28 |
| Primes of the form 4*10^n+1 and primes of the form 16*100^n+1 | enzocreti | enzocreti | 7 | 2019-05-05 13:19 |
| Primes of the Form Mod(p,q) = Mod(x,q) | a1call | Miscellaneous Math | 6 | 2018-12-11 03:34 |
| Primes of the form n+-phi(n) | carpetpool | carpetpool | 3 | 2017-01-26 01:29 |
