20190419, 23:05  #188  
"Robert Gerbicz"
Oct 2005
Hungary
2523_{8} Posts 
Quote:
Say 2^a divides p1 3^b divides p+5 ofcourse you want 2^a~3^b (~sqrt(N)) because then you know large p1,(p+6)1 factors in the oder of sqrt(N), so a=floor(log(N)/log(2)/2) b=floor(log(N)/log(3)/2) you can search p in the form (because 2^a and 3^b are coprime): p=u*2^a+v*3^b, from divisibilities you can get: Code:
v*3^b==1 mod 2^a u*2^a==5 mod 3^b 

20190419, 23:19  #189  
Sep 2002
Database er0rr
17×193 Posts 
Quote:
Last fiddled with by paulunderwood on 20190419 at 23:22 

20190419, 23:31  #190  
"Serge"
Mar 2008
Phi(3,3^1118781+1)/3
21544_{8} Posts 
Quote:
Surely now, 10 years later, one can repeat Ken's trick to find a couple 40,000digit sexy primes. I added a little friendly competition thread. Have some fun! 

20190420, 02:06  #191  
Jun 2015
Vallejo, CA/.
2^{2}·239 Posts 
Quote:
YepI And that is what we call a triplet, which at least for large enough numbers is more important than just a pair of sexy primes. 😋 

20190422, 02:47  #192  
"Serge"
Mar 2008
Phi(3,3^1118781+1)/3
2^{2}·3·5·151 Posts 
Quote:


20190911, 11:45  #194 
Sep 2002
Database er0rr
17·193 Posts 
Congrats to Ryan for a top20 prime 7*6^6772401+1 (5269954 digits)

20190918, 16:59  #195 
Dec 2011
After milion nines:)
5·257 Posts 
Small but sweet :)
[Worker #1 Sep 18 17:41:47] 9*10^380734+1 is a probable prime! Wh8: 0976AF3D,00000000 And of course it is proven prime with LLR :) Last fiddled with by pepi37 on 20190918 at 16:59 
20200304, 03:02  #196 
Jun 2015
Vallejo, CA/.
2^{2}·239 Posts 
This one has not been yet verified but it looks genuine.
6962 · 31^{2863120}  1 4269952 Digits. Largest of the year. Will rank 20 if verified. https://primes.utm.edu/primes/page.php?id=130702 Last fiddled with by VBCurtis on 20200304 at 03:06 Reason: Fixed exponent rendering 
20200313, 15:21  #197 
Sep 2002
Database er0rr
17×193 Posts 
Congrats to Ryan Propper for his recent batch of proth mega primes for k = 9, 11 and 13 the largest of which has 3,462,100 digits
Last fiddled with by paulunderwood on 20200313 at 15:22 
20200316, 17:13  #198  
"Jeppe"
Jan 2016
Denmark
2^{3}×3×5 Posts 
Quote:
/JeppeSN 

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