20190625, 22:21  #23  
"Composite as Heck"
Oct 2017
5×11^{2} Posts 
Quote:
Quote:
~52 days on a Radeon VII, much longer on a standard desktop. 

20190626, 00:16  #24 
Sep 2002
Database er0rr
3^{2}×7×53 Posts 
52 days for someone with one of these beasts might be worth the run!
Code:
forprime(p=7,665972737,X=lift(Mod(2,p^21)^p);e=X%(p1);E=X%(p); r=lift(lift(Mod(Mod(1,p)*x,x^24*x+1)^(e))); R=lift(lift(Mod(Mod(1,p)*x,x^24*x+1)^(E))); if(r==1&&R==x,print([p,r,R,e,E]))) [665972737, 1, x, 631635968, 648804353] Reminder: it is a factor of S_{8}, Last fiddled with by paulunderwood on 20190626 at 01:02 
20190626, 11:51  #25 
Sep 2002
Database er0rr
3^{2}×7×53 Posts 
If Mod(Mod(1,p)*x,x^24*x+1)^lift(Mod(2,p^21)^p)==1 then the properties to be checked are:
kronecker(3,p)==1 then Mod(Mod(1,p)*x,x^24*x+1)^(lift(Mod(2,p^21)^p)%p)==x kronecker(3,p)==1 then Mod(Mod(1,p)*x,x^24*x+1)^(lift(Mod(2,p^21)^p)%p)==x+4 I plan to write a GMP+primesieve program using the S_{i} sequence to extend the list in the OP. Last fiddled with by paulunderwood on 20190627 at 02:14 
20190626, 23:18  #26 
Sep 2002
Database er0rr
110100001011_{2} Posts 
I made a mistake in the above post, in the first line, which I have edited from p1 to p^21.
I checked MM127 i,e. p=170141183460469231731687303715884105727 Code:
? Mod(Mod(1,p)*x,x^24*x+1)^(lift(Mod(2,p^21)^p)) Mod(Mod(1, 170141183460469231731687303715884105727), x^2  4*x + 1) ? Mod(Mod(1,p)*x,x^24*x+1)^(lift(Mod(2,p^21)^p)%p) Mod(Mod(170141183460469231731687303715884105726, 170141183460469231731687303715884105727), x^2  4*x + 1) ? Mod(Mod(1,p)*x,x^24*x+1)^(lift(Mod(2,p^21)^p)%(p1)) Mod(Mod(4, 170141183460469231731687303715884105727)*x + Mod(170141183460469231731687303715884105726, 170141183460469231731687303715884105727), x^2  4*x + 1) Last fiddled with by paulunderwood on 20190626 at 23:20 
20190627, 00:02  #27 
Sep 2002
Database er0rr
3^{2}·7·53 Posts 
There is a fissure in this test for MM (double mersenne) numbers as MM19 passes the test and is not prime
I will now focus on primes in the factorization of S_{i} which are not of the form 2^p1. Last fiddled with by paulunderwood on 20190627 at 00:05 
20190627, 11:16  #28  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT)
1011001000000_{2} Posts 
Quote:
Are you suggesting that this is a test faster than prp that will determine that some numbers are composites(looks like not 2^p1)? 

20190627, 12:03  #29  
Sep 2002
Database er0rr
3^{2}×7×53 Posts 
Quote:
I think it tests prime factors p of the sequence S_{i} = S_{i1}^22 where the inititial value is 4  the one used in the LL test. I exclude 2 and 2^q1 as factors. I now have new criteria: Code:
Mod(Mod(1,p)*x,x^24*x+1)^(lift(Mod(2,p^21)^(p))) == 1 Mod(Mod(1,p)*x,x^24*x+1)^(lift(Mod(2,p^21)^(p))+1) == x The GMP+primesieve program searching for such factors is running. If I find a factor p with the above criteria and the corresponding Mp factors with factor5 my idea will be debunked. Last fiddled with by paulunderwood on 20190627 at 12:42 

20190627, 13:28  #30  
Sep 2002
Database er0rr
6413_{8} Posts 
Quote:
Last fiddled with by paulunderwood on 20190627 at 13:30 

20190627, 14:34  #31 
Sep 2002
Database er0rr
3^{2}·7·53 Posts 
M665972737
Is anyone testing or about to test M665972737? If so are you using a GPU? If no one is testing it, I will schedule it on a 4 core AVX2 box running mprime. I see that jimihimsimi booked it out in 2016. Is this stale? Would I be poaching it?
Last fiddled with by paulunderwood on 20190627 at 14:35 
20190627, 14:41  #32  
Jun 2003
2^{6}·73 Posts 
Quote:


20190627, 14:45  #33 
Sep 2002
Database er0rr
3^{2}·7·53 Posts 
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?
Last fiddled with by paulunderwood on 20190627 at 15:03 
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