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Old 2019-04-15, 16:50   #1
enzocreti
 
Mar 2018

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Default Prime 5101

The prime 5101 is congruent to 3^6 (mod 1093)




Are there infinitely many primes p congruent to 3^k (mod 1093) with k>0?
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Old 2019-04-15, 17:01   #2
CRGreathouse
 
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Aug 2006

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Quote:
Originally Posted by enzocreti View Post
Are there infinitely many primes p congruent to 3^k (mod 1093) with k>0?
For any positive integer k there are infinitely many primes congruent to 3^k mod 1093, yes. Note that 3 is relatively prime to 1093 (and that 3^k has order 7 mod 1093).

Last fiddled with by CRGreathouse on 2019-04-15 at 17:02
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Old 2019-04-15, 17:16   #3
enzocreti
 
Mar 2018

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Default 5101

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Originally Posted by CRGreathouse View Post
For any positive integer k there are infinitely many primes congruent to 3^k mod 1093, yes. Note that 3 is relatively prime to 1093 (and that 3^k has order 7 mod 1093).



51001 divides 2^(5101-1)-1.


Just a curio


But maybe a better curio is that 1021 and 1201 divide 2^(5101-1)-1 where 1021 and 1201 are primes with 0 and 2 changed....1021+1201 is 2222...moreover 1801 and 8101 divide 2^5100-1...also here 8 and 1 changed

Last fiddled with by enzocreti on 2019-04-15 at 17:52
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Old 2019-04-15, 18:14   #4
enzocreti
 
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Default Amazing that...

(2^5100-1)/1021/1201/1801/8101 is congruent to 9393 mod (101^2)




(2^5100-1) is divisible by at least four primes of the form x^2+45*y^2

Last fiddled with by enzocreti on 2019-04-15 at 18:28
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