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Old 2019-06-25, 22:21   #23
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Quote:
Originally Posted by paulunderwood View Post
M58133053441 has no factors below 2^81.

There is not much hope that this number can be LL/PRP'ed in the near future. Even is the software existed it would require a big iron machine to be tied up for decades.
If gpuowl could go this high it would take a single Radeon VII ~1090 years with p^2 scaling.

Quote:
Originally Posted by hansl View Post
Well, yeah to put things in perspective it has ~6.77x as many bits as F33, which is still out of reach.
~24 years on a Radeon VII if the fermat number test is roughly as optimisable as the Mp PRP.

Quote:
Originally Posted by paulunderwood View Post
Out of curiosity, how long would it take to test M665972737 on an average AVX2 desktop?
~52 days on a Radeon VII, much longer on a standard desktop.
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Old 2019-06-26, 00:16   #24
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52 days for someone with one of these beasts might be worth the run!

Code:
forprime(p=7,665972737,X=lift(Mod(2,p^2-1)^p);e=X%(p-1);E=X%(p);
r=lift(lift(Mod(Mod(1,p)*x,x^2-4*x+1)^(e)));
R=lift(lift(Mod(Mod(1,p)*x,x^2-4*x+1)^(E)));
if(r==1&&R==x,print([p,r,R,e,E])))

[665972737, 1, x, 631635968, 648804353]
665972737 is the first prime with these properties.

Reminder: it is a factor of S8,

Last fiddled with by paulunderwood on 2019-06-26 at 01:02
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Old 2019-06-26, 11:51   #25
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If Mod(Mod(1,p)*x,x^2-4*x+1)^lift(Mod(2,p^2-1)^p)==1 then the properties to be checked are:

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

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

I plan to write a GMP+primesieve program using the Si sequence to extend the list in the OP.

Last fiddled with by paulunderwood on 2019-06-27 at 02:14
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Old 2019-06-26, 23:18   #26
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I made a mistake in the above post, in the first line, which I have edited from p-1 to p^2-1.

I checked MM127 i,e. p=170141183460469231731687303715884105727

Code:
? Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^p))

Mod(Mod(1, 170141183460469231731687303715884105727), x^2 - 4*x + 1)

? Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^p)%p)

Mod(Mod(170141183460469231731687303715884105726, 170141183460469231731687303715884105727), x^2 - 4*x + 1)

? Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^p)%(p-1))

Mod(Mod(4, 170141183460469231731687303715884105727)*x + Mod(170141183460469231731687303715884105726, 170141183460469231731687303715884105727), x^2 - 4*x + 1)
It looks like MM127 is prime!

Last fiddled with by paulunderwood on 2019-06-26 at 23:20
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Old 2019-06-27, 00:02   #27
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Quote:
Originally Posted by paulunderwood View Post

It looks like MM127 is prime!
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 Si which are not of the form 2^p-1.

Last fiddled with by paulunderwood on 2019-06-27 at 00:05
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Old 2019-06-27, 11:16   #28
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Quote:
Originally Posted by paulunderwood View Post
I made a mistake in the above post, in the first line, which I have edited from p-1 to p^2-1.

I checked MM127 i,e. p=170141183460469231731687303715884105727

Code:
? Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^p))

Mod(Mod(1, 170141183460469231731687303715884105727), x^2 - 4*x + 1)

? Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^p)%p)

Mod(Mod(170141183460469231731687303715884105726, 170141183460469231731687303715884105727), x^2 - 4*x + 1)

? Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^p)%(p-1))

Mod(Mod(4, 170141183460469231731687303715884105727)*x + Mod(170141183460469231731687303715884105726, 170141183460469231731687303715884105727), x^2 - 4*x + 1)
It looks like MM127 is prime!
How long did this take?

Are you suggesting that this is a test faster than prp that will determine that some numbers are composites(looks like not 2^p-1)?
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Old 2019-06-27, 12:03   #29
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Quote:
Originally Posted by henryzz View Post
How long did this take?

Are you suggesting that this is a test faster than prp that will determine that some numbers are composites(looks like not 2^p-1)?
it is a very quick test -- less than a second.

I think it tests prime factors p of the sequence Si = Si-1^2-2 where the inititial value is 4 -- the one used in the LL test. I exclude 2 and 2^q-1 as factors.

I now have new criteria:

Code:
Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^(p))) == 1
Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^(p))+1) == x
I think the first criterion is always me by such p, so I only have to test the second.

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 2019-06-27 at 12:42
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Old 2019-06-27, 13:28   #30
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Quote:
Originally Posted by paulunderwood View Post
it is a very quick test -- less than a second.

I think it tests prime factors p of the sequence Si = Si-1^2-2 where the inititial value is 4 -- the one used in the LL test. I exclude 2 and 2^q-1 as factors.

I now have new criteria:

Code:
Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^(p))) == 1
Mod(Mod(1,p)*x,x^2-4*x+1)^(lift(Mod(2,p^2-1)^(p))+1) == x
I think the first criterion is always me by such p, so I only have to test the second.

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.
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.

Last fiddled with by paulunderwood on 2019-06-27 at 13:30
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Old 2019-06-27, 14:34   #31
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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 2019-06-27 at 14:35
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Old 2019-06-27, 14:41   #32
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Quote:
Originally Posted by paulunderwood View Post
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?
Needs a proper P-1 first.
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Old 2019-06-27, 14:45   #33
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Quote:
Originally Posted by axn View Post
Needs a proper P-1 first.
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 2019-06-27 at 15:03
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