20190415, 16:50  #1 
Mar 2018
523 Posts 
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? 
20190415, 17:01  #2 
Aug 2006
1011100100101_{2} Posts 
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 20190415 at 17:02 
20190415, 17:16  #3  
Mar 2018
523 Posts 
5101
Quote:
51001 divides 2^(51011)1. Just a curio But maybe a better curio is that 1021 and 1201 divide 2^(51011)1 where 1021 and 1201 are primes with 0 and 2 changed....1021+1201 is 2222...moreover 1801 and 8101 divide 2^51001...also here 8 and 1 changed Last fiddled with by enzocreti on 20190415 at 17:52 

20190415, 18:14  #4 
Mar 2018
1000001011_{2} Posts 
Amazing that...
(2^51001)/1021/1201/1801/8101 is congruent to 9393 mod (101^2)
(2^51001) is divisible by at least four primes of the form x^2+45*y^2 Last fiddled with by enzocreti on 20190415 at 18:28 
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