mersenneforum.org primes : 270*(1000^1-1)/999+1
 Register FAQ Search Today's Posts Mark Forums Read

 2019-05-07, 20:59 #1 enzocreti   Mar 2018 2×3×5×17 Posts primes : 270*(1000^1-1)/999+1 primes of the shape: 270*(1000^n-1)/999+1 it turned out that for n=1483 (prime) the number 270*(1000^1483-1)/999+1 is prime. 1483 is congruent to 128 mod 271. so the question is when n is prime and 270*(1000^n-1)/999+1 is prime, n must be congruent to 2^k mod 271?
 2019-05-08, 01:57 #2 CRGreathouse     Aug 2006 11·13·41 Posts It doesn't seem likely. What do you think?
 2019-05-08, 13:09 #3 enzocreti   Mar 2018 2·3·5·17 Posts What do you think about this my mathexchange great apreciated question ? https://math.stackexchange.com/quest...70270271-prime the number is prime for the following values of n: 1,2,3,9,12,129,740,788,1483,7964 I see that when n is odd and multiple of 3, then n-1 is a 2nd power...when n is even>2, then n-1 is a prime and even an emirp! Last fiddled with by enzocreti on 2019-05-08 at 13:22
 2019-05-08, 15:41 #4 enzocreti   Mar 2018 2·3·5·17 Posts emirps I see also that emirps 11,739,787 and 7963 are of the shape 8k+3.
2019-05-09, 07:03   #5
enzocreti

Mar 2018

7768 Posts
forms of the primes

Quote:
 Originally Posted by enzocreti I see also that emirps 11,739,787 and 7963 are of the shape 8k+3.

The exponents leading to a prime are n=1,2,3,9,12,129,740,788,1483,7964

When n is prime>2 (3 and 1483), 3 and 1483 are primes of the shape 8s+3. Can other shapes ruled out?
When n is even>2, then (n-1) is an emirp of the shape 8s+3. Can other shapes ruled out?

 2019-05-09, 11:02 #6 enzocreti   Mar 2018 1FE16 Posts next term n=7964 is the last exponent found leading to a prime... which do you guess it could be the next exp leading to a prime? How large could it be, what magnitude? Last fiddled with by enzocreti on 2019-05-09 at 11:02
 2019-05-09, 12:52 #7 enzocreti   Mar 2018 2×3×5×17 Posts ...emirps the emirps 11, 739, 787, 7963 are also of the form 2*x^2+11*y^2

 Similar Threads Thread Thread Starter Forum Replies Last Post storm5510 Software 1 2018-09-29 13:23 ramgeis PrimeNet 2 2014-04-08 10:27 Flatlander Riesel Prime Data Collecting (k*2^n-1) 17 2009-01-28 16:57 nuggetprime Riesel Prime Search 2 2007-04-09 11:44 GP2 Data 15 2004-06-11 01:57

All times are UTC. The time now is 06:33.

Sat Aug 8 06:33:50 UTC 2020 up 22 days, 2:20, 1 user, load averages: 1.59, 1.89, 1.91