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Forum: Miscellaneous Math 2021-04-09, 19:21
Replies: 35
Views: 638
Posted By paulunderwood
Whatever you do with 1+1+1+..+1+2 selfridges...

Whatever you do with 1+1+1+..+1+2 selfridges there will always be counterexamples if you allow a free parameter. I am not saying there will not exist counterexamples for 1+1+1..+1+2+2 -- they are...
Forum: Miscellaneous Math 2021-04-09, 00:41
Replies: 35
Views: 638
Posted By paulunderwood
Nice try. n==3 mod 4 has no counterexample for...

Nice try. n==3 mod 4 has no counterexample for the two selfridges test (2+i)^(n+1)==5 mod (n,i^2+1) for n<2^50.
Forum: Miscellaneous Math 2021-04-06, 14:35
Replies: 35
Views: 638
Posted By paulunderwood
Can you express your algorithm in Pari/GP for us?...

Can you express your algorithm in Pari/GP for us? Then it will be easier to understand and easier to test (to destruction).

If you are working over the complex numbers then raising the base a+b*i...
Forum: Miscellaneous Math 2021-04-03, 23:47
Replies: 35
Views: 638
Posted By paulunderwood
Please give us a worked example for the prime 97....

Please give us a worked example for the prime 97. :smile:
Forum: Tales From the Crypt(o) 2021-04-03, 21:55
Replies: 280
Views: 66,368
Posted By paulunderwood
Our beloved leader (in the UK) is going to...

Our beloved leader (in the UK) is going to propose "Covid Passports", a Chinese-like control of the population surreptitiously under the guise of "using every tool in the toolbox to restore the...
Forum: Factoring 2021-04-02, 20:31
Replies: 18
Views: 494
Posted By paulunderwood
I have been Windows-free for at least 20 years. I...

I have been Windows-free for at least 20 years. I started out on a ZX81; at Uni used PRIMOS and a DEC VAX system. For my sins I had to use DOS and completed rejected Windows during the 90's when it...
Forum: Factoring 2021-04-01, 19:45
Replies: 18
Views: 494
Posted By paulunderwood
All Linux here. You'll find Linux easier to...

All Linux here. You'll find Linux easier to configure to best suit your needs, Be free!
Forum: GPU Computing 2021-03-22, 14:10
Replies: 3
Views: 305
Posted By paulunderwood
Apart from Ubuntu, Fedora is a better choice than...

Apart from Ubuntu, Fedora is a better choice than Centos,
Forum: Miscellaneous Math 2021-03-18, 21:53
Replies: 118
Views: 23,816
Posted By paulunderwood
odd r

Let a=2^r, r odd and minimal such that kronecker(a^2-1,n)==-1
Test1. Mod(a^2-1.n)^((n-1)/2)==-1
Test2. Mod(Mod(2*x,n),x^2-2*a*a+1)^((n+1)/2)==2*kronecker(a+1)


Interestingly counterexamples...
Forum: Miscellaneous Math 2021-03-18, 19:41
Replies: 118
Views: 23,816
Posted By paulunderwood
If n = 2^s+-3, letting b = 5 would mean 2^s-2...

If n = 2^s+-3, letting b = 5 would mean 2^s-2 would okay for a base or 2^s -8 would also be okay for a base, since neither are powers ;
of 2. So apart from these corner cases taking b=3 should be...
Forum: Miscellaneous Math 2021-03-18, 06:24
Replies: 118
Views: 23,816
Posted By paulunderwood
Getting back on track for this thread... ...

Getting back on track for this thread...


Let b != +-2^s
Let a = b^r where kronecker(a^2-1,n) == -1
Test1: (a^2-1,n)^((n-1)/2) == -1 (mod n)
Test2: (b*x)^((n+1)/2) ==...
Forum: Miscellaneous Math 2021-03-17, 11:07
Replies: 58
Views: 1,375
Posted By paulunderwood
http://www.numbertheory.org/ntw/N6.html ...

http://www.numbertheory.org/ntw/N6.html

http://www.numbertheory.org/ntw/N7.html

Why do you not attach it here at MeresenneForum first? At least we can advise you on spelling and typographic...
Forum: Software 2021-03-15, 22:20
Replies: 12
Views: 354
Posted By paulunderwood
Hmm, two workers would do it. Then try four and...

Hmm, two workers would do it. Then try four and compare throughput.

I think mprime and the Linux scheduler are smart enough to set the right affinities.
Forum: Software 2021-03-15, 20:53
Replies: 12
Views: 354
Posted By paulunderwood
Try 2 instances of 26 cores each, one for each...

Try 2 instances of 26 cores each, one for each CPU. And then try 4 instances of 13 cores each and compare throughputs.
Forum: GPU Computing 2021-03-15, 20:39
Replies: 365
Views: 61,736
Posted By paulunderwood
You should be able to afford it if you find the...

You should be able to afford it if you find the next Mersenne prime :wink:
Forum: And now for something completely different 2021-03-15, 16:58
Replies: 48
Views: 16,700
Posted By paulunderwood
Talking Reserving: M86137 cofactor prp25896 M86371...

Reserving:

M86137 cofactor prp25896
M86371 cofactor prp25984
M87691 cofactor prp26371
E(11848)/(5*1582043) prp40792
Forum: Miscellaneous Math 2021-03-14, 14:25
Replies: 118
Views: 23,816
Posted By paulunderwood
No, it was not the question at the beginning of...

No, it was not the question at the beginning of the topic.

With only 51 known Mersenne prime < ~25 million digits and your condition being neccesary, we will probably never know of a contradiction...
Forum: Miscellaneous Math 2021-03-14, 11:33
Replies: 118
Views: 23,816
Posted By paulunderwood
Have you noticed that for prime Mp then...

Have you noticed that for prime Mp then 3^((Mp-1)/p)==2^r mod Mp for some r? Here 3 is not special. It works for all bases.

Anyway this thread was about working (mod n, f) where f is a quadratic...
Forum: Other Mathematical Topics 2021-03-11, 19:31
Replies: 27
Views: 812
Posted By paulunderwood
3 is special because kronecker(3,Mp)==-1 for all...

3 is special because kronecker(3,Mp)==-1 for all odd p.

Lehmer's test (https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test) is an efficient implementation of...
Forum: Programming 2021-03-08, 18:01
Replies: 11
Views: 661
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: 11
Views: 661
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: 11
Views: 661
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: 11
Views: 661
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: 241
Views: 40,691
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: 209
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
Showing results 1 to 25 of 1000

 
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