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2019-06-27, 16:20   #34
GP2

Sep 2003

A1316 Posts

Quote:
 Originally Posted by paulunderwood Is 8GB RAM a problem? Please post the worktodo.txt file for this and the PRP test. Or does mprime write this file from its menu?
You could probably get the P−1 line from the Manual Assignment page.

You would normally get the PRP line the same way, but it won't give it out since there's an old dead LL test still assigned.

Code:
PRP=N/A,1,2,665972737,-1,87,0
You could force a type-1 residue by adding ,3,1 to the end, or a type-4 residue by adding ,3,4 to the end. But no need, since it's a first-time test.

2019-06-27, 18:23   #35
paulunderwood

Sep 2002
Database er0rr

23×3×139 Posts

Quote:
 Originally Posted by GP2 You could probably get the P−1 line from the Manual Assignment page. You would normally get the PRP line the same way, but it won't give it out since there's an old dead LL test still assigned. Code: PRP=N/A,1,2,665972737,-1,87,0 You could force a type-1 residue by adding ,3,1 to the end, or a type-4 residue by adding ,3,4 to the end. But no need, since it's a first-time test.
Thanks. I get the following error code for P-1 assignments:

Quote:
 Error code: 40 Error text: No assignment available meeting CPU, program code and work preference requirements, cpu_id: 1672742, cpu # = 0, user_id = 170463
So I have jumped straight in with a PRP test. If somebody else wants to do the P-1, please go ahead.

Code:
[Work thread Jun 27 19:30] Iteration: 10000 / 665972737 [0.00%], ms/iter: 82.912, ETA: 639d 01:55

Last fiddled with by paulunderwood on 2019-06-27 at 18:32

2019-06-27, 19:26   #36
GP2

Sep 2003

2,579 Posts

Quote:
 Originally Posted by paulunderwood Thanks. I get the following error code for P-1 assignments: So I have jumped straight in with a PRP test. If somebody else wants to do the P-1, please go ahead.
You can also try https://www.mersenne.ca/prob.php to get a plausible P−1 line.

I have started the P−1 test. However Primenet doesn't register an assignment. It might take 10 days or so.

2019-06-27, 19:29   #37
paulunderwood

Sep 2002
Database er0rr

64108 Posts

Quote:
 Originally Posted by GP2 You can also try https://www.mersenne.ca/prob.php to get a plausible P−1 line. I have started the P−1 test. However Primenet doesn't register an assignment. It might take 10 days or so.

2019-06-27, 20:35   #38
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

2·13·53 Posts

Quote:
 Originally Posted by paulunderwood With the EFF award in mind, I am running this program: Code: forprime(q=1,100000000000,s=Mod(1416317954,q);for(k=7,33,s=s^2-2;if(s==2,print([q,k-2]);break)))
You are mixing lots of things in different ways.
1. if s=2, then it remains s=2 after x->x^2-2, and we're seeking 0 for LLT, but that would be still crackpot, because q doesn't divide Mq, the modulus used in LLT.
2. yes we see that 607 is in the sequence by a totally wrong method, you got a strong law of small number hit.
3.
you can check that S[n]-2=(S[n-1]-2)*S[n-2]^2 (this is also the heart of the Jacobi check in the LLT), so the new factors come from S[n-2]. It is provable (if I'm not wrong), that the odd prime factors of S[m] has got p=k*2^(m+2)+-1 form.

2019-06-27, 20:52   #39
paulunderwood

Sep 2002
Database er0rr

333610 Posts

Quote:
 Originally Posted by R. Gerbicz 2. yes we see that 607 is in the sequence by a totally wrong method, you got a strong law of small number hit.
I have been agonizing over this for days. Yes it seems the law of small numbers holds -- except if you check Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^p)%p)== x or -x+4 for all primes below some largish bound they are not as dense as they are in the sequence given in the OP.

2019-06-27, 23:06   #40
paulunderwood

Sep 2002
Database er0rr

23·3·139 Posts

Quote:
 Originally Posted by paulunderwood These new criteria are always met for p|Si. I so I am using the previous ones given earlier on -- in post 25 of this thread.
I wish to re-instate the criterion -- slightly modified -- of non-2^q-1 prime p|Si being:

if kronecker(3,p)==1 check Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^p-1)%p) == 1

if kronecker(3,p)==-1 check Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^p+1)%p) == 1

Or combining the two:

Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^p-kronecker(3,p))%p) == 1

2019-06-30, 09:20   #41
lavalamp

Oct 2007
London, UK

130010 Posts

Quote:
 Originally Posted by paulunderwood 52 days for someone with one of these beasts might be worth the run!
If you are convinced it is prime as you say, then $680 for a Radeon VII to win$150,000 seems worth it to you. Perhaps you should put your money where your mouth is.

Edit: In fact, with such a payoff, one only needs to be 0.5% sure it is prime for it to be a good bet...

Last fiddled with by lavalamp on 2019-06-30 at 09:36

2019-06-30, 10:31   #42
paulunderwood

Sep 2002
Database er0rr

23×3×139 Posts

Quote:
 Originally Posted by lavalamp If you are convinced it is prime as you say, then $680 for a Radeon VII to win$150,000 seems worth it to you. Perhaps you should put your money where your mouth is. Edit: In fact, with such a payoff, one only needs to be 0.5% sure it is prime for it to be a good bet...
Maybe I should have kept my mouth shut! And it is $50k USD. I am testing it with an ETA of 471 days. I am not 100% sure it is prime -- if it is then the 20 billion one is likely to be too and that's worth$250k USD.

Last fiddled with by paulunderwood on 2019-06-30 at 10:36

2019-06-30, 17:29   #43
paulunderwood

Sep 2002
Database er0rr

23×3×139 Posts

Quote:
 Originally Posted by paulunderwood Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^p-kronecker(3,p))%p) == 1
Code:
count=32;size=2^8;for(test=1,count,sample=random(size+1);if(sample%size==0,print([test])))
The "count" is representative of the original OP size; 2^8 reflects S8. The chance of a "zero" (or any other more suitable value) on "%p" is very small. What does a real statistician say about this? Note 8 becomes 20. (Please bear in mind any effects of the form k*2^(m+2)+-1 as pointed out by Robert Gerbicz.)

Last fiddled with by paulunderwood on 2019-06-30 at 20:56

2019-06-30, 17:57   #44
lavalamp

Oct 2007
London, UK

22×52×13 Posts

Quote:
 Originally Posted by paulunderwood And it is \$50k USD.
With GIMPS and Prime95 it is, due to how the prize is shared. I do not know if there is such an arrangement with gpuowl.

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