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Old 2019-06-24, 07:39   #12
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Quote:
Originally Posted by hansl View Post
OK, i'm ~70% done with 75-76. And I've started 77-78 and 78-79 on other boxes.

BTW, I can't wait to upgrade one of my workstations. I recently ordered parts to take it from 6C/12T up to (dual socket) 24C/48T ... 4x the cores
Opened another box with 79 to 80 bits.
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Old 2019-06-24, 08:40   #13
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Quote:
Originally Posted by paulunderwood View Post
Opened another box with 79 to 80 bits.
76-77 done. No factors.

Doing 80-81 bits now.
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Old 2019-06-24, 14:28   #14
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Quote:
Originally Posted by paulunderwood View Post
76-77 done. No factors.

Doing 80-81 bits now.
No factors from 75-76 (not sure if you saw in my previous edited post)
No factors from 77-78
No factors from 78-79

With that I'm done with this diversion for now; back to my regularly scheduled crunching.
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Old 2019-06-25, 06:21   #15
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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.
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Old 2019-06-25, 08:08   #16
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Well, yeah to put things in perspective it has ~6.77x as many bits as F33, which is still out of reach.
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Old 2019-06-25, 15:09   #17
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Quote:
forprime(q=1,100000000000,s=Mod(1416317954,q);for(k=7,33,s=s^2-2;if(s==2,print([q,k-2]);break)))
Where did you get this algorithm from? Why do you think M58133053441 might be prime because S17 = 0 when S0 = 1416317954 ?
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Old 2019-06-25, 15:43   #18
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Quote:
Originally Posted by paulunderwood View Post
<snip>
forprime(q=1,100000000000,s=Mod(1416317954,q);for(k=7,33,s=s^2-2;if(s==2,print([q,k-2]);break)))
<snip>
OK, I'll bite: Why does k begin at 7?

Code:
s=4;for(i=1,4,s=s^2-2;print(s))
14
194
37634
1416317954
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Old 2019-06-25, 16:24   #19
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Quote:
Originally Posted by ATH View Post
Where did you get this algorithm from? Why do you think M58133053441 might be prime because S17 = 0 when S0 = 1416317954 ?
Because S21 = 0 when S0=4 and s+2 is a prime i.e 23 -- it works for M607:

Code:
p=607;s=Mod(4,p);for(k=1,3,s=s^2-2;print(s))
Mod(14, 607)
Mod(194, 607)
Mod(0, 607)
5 is prime!

It also works for say 8191, but that is the value of a Mersenne prime.

Last fiddled with by paulunderwood on 2019-06-25 at 16:25
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Old 2019-06-25, 16:29   #20
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Quote:
Originally Posted by Dr Sardonicus View Post
OK, I'll bite: Why does k begin at 7?

Code:
s=4;for(i=1,4,s=s^2-2;print(s))
14
194
37634
1416317954
Normally we start at 3. Starting at 1416317954 saves a few iterations in a long program. I should have checked for s==0 instead that would have been quicker!
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Old 2019-06-25, 16:57   #21
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Code:
p=58133053441;e=lift(Mod(2,p^2-1)^p);Mod(Mod(1,p)*x,x^2-4*x+1)^(e)
Mod(Mod(1, 58133053441), x^2 - 4*x + 1)
But I cannot see how this helps.
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Old 2019-06-25, 18:37   #22
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Out of curiosity, how long would it take to test M665972737 on an average AVX2 desktop?

Code:
? p=665972737;e=lift(Mod(2,p^2-1)^p)%p;Mod(Mod(1,p)*x,x^2-4*x+1)^(e)
Mod(Mod(1, 665972737)*x, x^2 - 4*x + 1)
Which seems quite remarkable.

Additionally:

Code:
? p=607;e=lift(Mod(2,p^2-1)^p)%p;lift(lift(Mod(Mod(1,p)*x,x^2-4*x+1)^(e)))
606*x + 4
? p=60651732991;e=lift(Mod(2,p^2-1)^p)%p;lift(lift(Mod(Mod(1,p)*x,x^2-4*x+1)^(e)))
60651732990*x + 4

Last fiddled with by paulunderwood on 2019-06-25 at 19:18
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