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Old 2016-04-06, 19:05   #1
J F
 
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Default 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.
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Old 2016-04-06, 19:49   #2
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Attach the decimal expansion in a file and I will check it out for you.
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Old 2016-04-06, 20:15   #3
J F
 
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Quote:
Originally Posted by paulunderwood View Post
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
File Type: 7z 7816-30157digits.7z (2.7 KB, 33 views)
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Old 2016-04-06, 20:29   #4
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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
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Old 2016-04-06, 20:56   #5
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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.
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Old 2016-04-06, 21:10   #6
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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
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Old 2016-04-06, 21:22   #7
J F
 
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Thanks!
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Old 2016-04-06, 23:02   #8
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Quote:
Originally Posted by paulunderwood View Post
(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)
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Old 2016-04-07, 03:16   #9
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Quote:
Originally Posted by paulunderwood View Post
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
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Old 2016-04-07, 19:19   #10
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Quote:
Originally Posted by a1call View Post
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.
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Old 2016-04-07, 19:22   #11
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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.
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