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Search: Posts Made By: paulunderwood
Forum: Programming 2021-03-08, 18:01
Replies: 10
Views: 227
Posted By paulunderwood
A week or two for Mersenne. Other forms take...

A week or two for Mersenne. Other forms take longer because they are not so simple in form and there is a special "transform" for Mersenne numbers,
Forum: Programming 2021-03-08, 17:51
Replies: 10
Views: 227
Posted By paulunderwood
For Python: https://pypi.org/project/labmath/ for...

For Python: https://pypi.org/project/labmath/ for example has various tests including bpsw and fermat_prp.

Once you have tried out 10k digit numbers be amazed by the speed of OpenPFGW (which like...
Forum: Programming 2021-03-08, 16:41
Replies: 10
Views: 227
Posted By paulunderwood
I don't know Python. I can't make heads nor tails...

I don't know Python. I can't make heads nor tails of it. Someone else will chip in.

Yes GWNUM does have that license agreement about world record primes. If you don't want to get your hands dirty...
Forum: Programming 2021-03-08, 16:12
Replies: 10
Views: 227
Posted By paulunderwood
These numbers are too large for prime searching...

These numbers are too large for prime searching with GMP. To do one PRP test takes ~30M mults of 10M digits by 10M digits (and mod reductions) without a very fast FFT as is used by GWNUM library...
Forum: Riesel Prime Search 2021-03-02, 18:52
Replies: 239
Views: 38,748
Posted By paulunderwood
Smile 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...
Forum: Miscellaneous Math 2021-03-01, 20:48
Replies: 2
Views: 126
Posted By paulunderwood
List of candidates by crazy formula

Based on the "test" lift(Mod(420,p^2-1)^p)%p==0 I get this partial list of exponents


3
5
7
11
13
17
19
Forum: Software 2021-02-28, 15:28
Replies: 8
Views: 453
Posted By paulunderwood
If you have tried llrCuda out please post how...

If you have tried llrCuda out please post how well it does. How many AVX2 cores is it equivalent to on a top end nVidia card?
Forum: Hardware 2021-02-28, 08:23
Replies: 166
Views: 16,818
Posted By paulunderwood
Can you run mprime on it out of the box or do you...

Can you run mprime on it out of the box or do you have to compile it to get it working on your Phi?
Forum: Hardware 2021-02-26, 13:13
Replies: 166
Views: 16,818
Posted By paulunderwood
There are a number of 56/60 22nm Xeon Phi on...

There are a number of 56/60 22nm Xeon Phi on ebay.co.uk at the moment for about £100. What are the adavantages? -- 60 GHz is lot; Do the have AVX2?. Apart from being 250w what are the...
Forum: Information & Answers 2021-02-24, 22:52
Replies: 20
Views: 508
Posted By paulunderwood
if it is divisible by n it leaves a remainder of...

if it is divisible by n it leaves a remainder of 0 by division which by definition is 0 mod n. After all n divides 0.

In my example 7!/(5!*2!). Don't forget not to divide by n. We have
...
Forum: Information & Answers 2021-02-24, 22:18
Replies: 20
Views: 508
Posted By paulunderwood
n! the numerator is divisible by n, but each of...

n! the numerator is divisible by n, but each of the factors of k! and (n-k)! are not.

Here is a concrete example 7!/(5!*2!). Here 7 divides 7! but not 5! or 2!
Forum: Information & Answers 2021-02-24, 21:10
Replies: 20
Views: 508
Posted By paulunderwood
I should have been more explicit: each of the...

I should have been more explicit: each of the factors of k! and (n-k)! are less than n which is assumed to be prime. n would not divide anything smaller. For example 7 does not divide 5!
Forum: Information & Answers 2021-02-24, 20:49
Replies: 20
Views: 508
Posted By paulunderwood
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...
Forum: Information & Answers 2021-02-24, 20:36
Replies: 20
Views: 508
Posted By paulunderwood
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...
Forum: Data 2021-02-24, 09:46
Replies: 549
Views: 75,359
Posted By paulunderwood
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.
Forum: Miscellaneous Math 2021-02-24, 09:13
Replies: 72
Views: 2,381
Posted By paulunderwood
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...
Forum: Data 2021-02-24, 06:42
Replies: 549
Views: 75,359
Posted By paulunderwood
@James, M82939 cofactor...

@James,

M82939 cofactor (https://primes.utm.edu/primes/page.php?id=132049) is certified prime
Forum: And now for something completely different 2021-02-24, 06:38
Replies: 47
Views: 14,769
Posted By paulunderwood
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)
Forum: Software 2021-02-23, 01:37
Replies: 12
Views: 3,716
Posted By paulunderwood
Exit mprime and in that directory run sudo chown...

Exit mprime and in that directory run sudo chown storm5510:storm5510 *. Then start mprime as non-root and no sudo.
Forum: Miscellaneous Math 2021-02-22, 21:03
Replies: 10
Views: 358
Posted By paulunderwood
2^13-1== 8191 is prime. 2^8191-1 is not. Easy to...

2^13-1== 8191 is prime. 2^8191-1 is not. Easy to check.
Forum: Software 2021-02-22, 17:06
Replies: 8
Views: 319
Posted By paulunderwood
Run top and press k (and kill the pid with...

Run top and press k (and kill the pid with SIGTERM?),
Forum: Miscellaneous Math 2021-02-22, 01:52
Replies: 10
Views: 358
Posted By paulunderwood
https://primes.utm.edu/mersenne/index.html#unknown...

https://primes.utm.edu/mersenne/index.html#unknown

Proving a ~10^51217599719369681875006054625051616349 digit number prime is beyond all known technolgy.
Forum: Miscellaneous Math 2021-02-21, 18:57
Replies: 18
Views: 1,091
Posted By paulunderwood
Question 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].
Forum: Miscellaneous Math 2021-02-21, 16:17
Replies: 18
Views: 1,091
Posted By paulunderwood
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&&
Forum: Miscellaneous Math 2021-02-21, 05:21
Replies: 18
Views: 1,091
Posted By paulunderwood
Question 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&&...
Showing results 1 to 25 of 1000

 
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