Forum: Riesel Prime Search
2021-03-02, 18:52
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Replies: 239
Views: 38,403
DRUG is PRP top
We had a nice email from Jeff Gilchrist this morning saying one of his computers had reported:
2^13380298-27 is base 3-Fermat PRP! (4027872 decimal digits) Time : 9677.550 sec.
2^13380298-27 is...
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Forum: Miscellaneous Math
2021-03-01, 20:48
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Replies: 2
Views: 119
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Forum: Software
2021-02-28, 15:28
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Replies: 8
Views: 417
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Forum: Hardware
2021-02-28, 08:23
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Replies: 162
Views: 16,100
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Forum: Hardware
2021-02-26, 13:13
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Replies: 162
Views: 16,100
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Forum: Information & Answers
2021-02-24, 22:52
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Replies: 20
Views: 450
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Forum: Information & Answers
2021-02-24, 22:18
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Replies: 20
Views: 450
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Forum: Information & Answers
2021-02-24, 21:10
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Replies: 20
Views: 450
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Forum: Information & Answers
2021-02-24, 20:49
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Replies: 20
Views: 450
Since for prime n we have a^n== a mod n then...
Since for prime n we have a^n== a mod n then a^(n-1) == 1. We can take a square root a^((n-1)/2) and expect the result to be +- 1. If it is 1 and we can take another square root by dividing the...
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Forum: Information & Answers
2021-02-24, 20:36
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Replies: 20
Views: 450
Surely you did the binomial theorem. (a+b)^n =...
Surely you did the binomial theorem. (a+b)^n = a^n + binom(n,1)*a^(n-1)*b + binom(n,2)*a^(n-2)*b^2 + ... + b^n. Now think about a particular binom(n,k). It is n!/(k!*(n-k)!). If n was prime then...
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Forum: Data
2021-02-24, 09:46
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Replies: 549
Views: 74,640
Thanks, Jean.
I merely got the candidate...
Thanks, Jean.
I merely got the candidate from www.mersenne.ca. I might have run a 3-PRP to be sure-ish. Anyway, Primo does a quick Fermat+Lucas à la BPSW before embarking on a lengthy ECPP path.
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Forum: Miscellaneous Math
2021-02-24, 09:13
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Replies: 72
Views: 2,268
Are you seriously thinking of spreading this...
Are you seriously thinking of spreading this calculation over a supercomputer running Mathematica? At the current wavefront you would need to calculate a polynomial with ~2^109000000 terms, let alone...
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Forum: Data
2021-02-24, 06:42
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Replies: 549
Views: 74,640
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Forum: And now for something completely different
2021-02-24, 06:38
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Replies: 47
Views: 14,469
M82939 cofactor is certified...
M82939 cofactor is certified (https://primes.utm.edu/primes/page.php?id=132049)
FactorDB entry (http://www.factordb.com/index.php?id=1100000000213099295)
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Forum: Software
2021-02-23, 01:37
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Replies: 12
Views: 3,582
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Forum: Miscellaneous Math
2021-02-22, 21:03
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Replies: 10
Views: 330
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Forum: Software
2021-02-22, 17:06
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Replies: 8
Views: 287
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Forum: Miscellaneous Math
2021-02-22, 01:52
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Replies: 10
Views: 330
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Forum: Miscellaneous Math
2021-02-21, 18:57
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Replies: 18
Views: 1,049
Big question
Are the solutions to b^2 = 2^i*3^j + 1 finite? (i, j >= 0)
I have only found b in [2, 3, 5 ,7, 17].
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Forum: Miscellaneous Math
2021-02-21, 16:17
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Replies: 18
Views: 1,049
Latest test:
...
Latest test:
{EulerPRP(a,n)=Mod(a,n)^((n-1)/2)==kronecker(a,n);}
{
tst(n,a)=
gcd(a+3,n)==1&&
gcd(3*a+1,n)==1&&
gcd(a^2+6*a+1,n)==1&&
kronecker(a,n)==-1&&
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Forum: Miscellaneous Math
2021-02-21, 05:21
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Replies: 18
Views: 1,049
All Euler-PRP = -1
I am now testing:
{tst(n,a)=kronecker(a,n)==-1&&kronecker(a-1,n)==-1&&kronecker(a+1,n)==-1&&
Mod(a,n)^((n-1)/2)==-1&&Mod(a-1,n)^((n-1)/2)==-1&&Mod(a+1,n)^((n-1)/2)==-1&&...
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Forum: Miscellaneous Math
2021-02-20, 18:28
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Replies: 72
Views: 2,268
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Forum: Riesel Prime Search
2021-02-19, 19:42
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Replies: 239
Views: 38,403
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Forum: Miscellaneous Math
2021-02-19, 11:20
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Replies: 72
Views: 2,268
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Forum: Miscellaneous Math
2021-02-19, 10:41
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Replies: 18
Views: 1,049
Rationale
The rationale for the above test:
Matrix: [a,a;1,a]
Characteristic eqn: y^2-2*a+a^2-a==0
Solutions: y = a +- sqrt(a)
"Strong" transform: z^2-2*(a+1)/(a-1)*z+1=0 and Euler-(a^2-a)==-1
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