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 2016-04-06, 19:05 #1 J F     Sep 2013 708 Posts PRP in A138957 There were some posts about https://oeis.org/A007908, so in case someone is interested in https://oeis.org/A138957 too: I got the 7816th term PRP, 30157 digits. It would be nice if someone could doublecheck. I went up to 39999 without another hit, so no other PRPs up to 70K-th term.
 2016-04-06, 19:49 #2 paulunderwood     Sep 2002 Database er0rr 3,491 Posts Attach the decimal expansion in a file and I will check it out for you.
2016-04-06, 20:15   #3
J F

Sep 2013

708 Posts

Quote:
 Originally Posted by paulunderwood Attach the decimal expansion in a file and I will check it out for you.
In case I messed up somewhere, does testing my file
qualify as valid doublecheck?
Attached Files
 7816-30157digits.7z (2.7 KB, 33 views)

 2016-04-06, 20:29 #4 paulunderwood     Sep 2002 Database er0rr 3,491 Posts For each a in {0,3,4,5,6,7} jacobiSymbol(a^2-4,n)==-1 and (x+a)^(n+1)==5+2*a (mod n, x^2-a*x+1)., which implies Euler-PRP tests base 5+2*a and associated Lucas PRP tests. Congrats on something that is almost certainly prime, modulo an ECPP check. Maybe you missed a PRP .... Last fiddled with by paulunderwood on 2016-04-06 at 20:46
 2016-04-06, 20:56 #5 J F     Sep 2013 3816 Posts What I meant is, yes, the number in the file is a PRP, but is it the 'right' number? For instance, bug in my string generation. A doublechecker should use its own.
 2016-04-06, 21:10 #6 paulunderwood     Sep 2002 Database er0rr 3,491 Posts Code: ? v=[];for(n=1,7816,d=digits(n);forstep(k=#d,1,-1,v=concat(v,d[k])));JF=read("../../Downloads/7816-30157digits.txt");digits(JF)==v 1 Last fiddled with by paulunderwood on 2016-04-06 at 21:11
 2016-04-06, 21:22 #7 J F     Sep 2013 23·7 Posts Thanks!
2016-04-06, 23:02   #8
paulunderwood

Sep 2002
Database er0rr

3,491 Posts

Quote:
 Originally Posted by paulunderwood (x+a)^(n+1)==5+2*a (mod n, x^2-a*x+1).,
Should have said: (x+2)^(n+1)==5+2*a (mod n, x^2-a*x+1)

2016-04-07, 03:16   #9
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

79316 Posts

Quote:
 Originally Posted by paulunderwood Congrats on something that is almost certainly prime, modulo an ECPP check.
Are large PRPs of any value/interest?
If so what sizes would be interesting?

Thank you in advance.

BTW that thread seems to be here:
http://www.mersenneforum.org/showthr...695#post415695

Last fiddled with by a1call on 2016-04-07 at 03:57

2016-04-07, 19:19   #10
CRGreathouse

Aug 2006

134628 Posts

Quote:
 Originally Posted by a1call Are large PRPs of any value/interest? If so what sizes would be interesting?
No particular value afaik, but if they're larger than 41169 digits they are large enough to make Henri Lifchitz & Renaud Lifchitz's PRP Records page.

 2016-04-07, 19:22 #11 paulunderwood     Sep 2002 Database er0rr 3,491 Posts http://www.primenumbers.net/prptop/p...p?page=40#haut You can enter "page" beyond "40", so that the actual lower limit is now 20k digits for submissions.