Te$ting billion digit number$

[paulunderwood]

With the EFF award in mind, I am running this program:

forprime(q=1,100000000000,s=Mod(1416317954,q);for(k=7,33,s=s^2-2;if(s==2,print([q,k-2]);break)))
[2, 5]
[3, 5]
[7, 5]
[31, 5]
[97, 5]
[127, 7]
[607, 5]
[8191, 13]
[12289, 10]
[22783, 8]
[131071, 17]
[265471, 8]
[524287, 19]
[592897, 8]
[1310719, 18]
[21757951, 18]
[29687809, 14]
[39845887, 21]
[665972737, 10]
[708158977, 6]
[2147483647, 31]
[2210398207, 22]
[2543310079, 8]
[58133053441, 23]
[60651732991, 21]

I am interested in the penultimate result because it has "k-2=23". How long would it take an average AVX2 box to test it as a Mp? It has ~20 billion digits.

(Note that 97 is there because k starts at 7.)

[GP2]

Originally Posted by paulunderwood

How long would it take an average AVX2 box to test it as a Mp? It has ~20 billion digits.

You're gonna need a bigger box.

[a1call]

This thread reminds me of a very old Sci-Fi novel that I never read myself but was told about by a friend:
Person A: They have spaceships that can travel to the Moon.
Person B: That's impossible. The power required for such a trip is enormous.
Person A: Yes, but they are using steam-engines to power their ships.

[chalsall]

Originally Posted by a1call

Person A: Yes, but they are using steam-engines to power their ships.

Please forgive me for this, but I read The Mote in God's Eye as a child.

I fail to understand why SETI listens for low-band microwaves when higher frequency photons are more likely to be used for long distant communications.

Maybe I'm just stupid. A non-zero probably.

[a1call]

At the risk of further off tracking, I agree that SETI is based on assuming the ET to have mastered capabilities that we did not possess a mere 200 years ago such as radio communication as well as Amplitude-Modulation which is only one of the many different possibilities of using electromagnetic waves, Yes there are more probable means than used by SETI. But that's a Can-of-Worms best left unopened in a Wikipedia-Obsessed, Democratically-Dictated-Science, audience.

[paulunderwood]

One more datum:

[87075848191, 21]

Its corresponding Mp is composite.

[paulunderwood]

? p=58133053441;for(k=1,1000000000,if(Mod(2,2*k*p+1)^p==1,print(k)))
? ##
  ***   last result computed in 25min, 51,820 ms.

The exponent has 36 bits. Both mlucas and mprime are limited to something below this. Can GPUs handle the trial factoring?

[R. Gerbicz]

Originally Posted by paulunderwood

The exponent has 36 bits. Both mlucas and mprime are limited to something below this. Can GPUs handle the trial factoring?

Surely, ~64 bits mutliplication isn't that hard, when there are existing gpu codes that are multiplying multimillion bits numbers.

[hansl]

Originally Posted by paulunderwood

? p=58133053441;for(k=1,1000000000,if(Mod(2,2*k*p+1)^p==1,print(k)))
? ##
  ***   last result computed in 25min, 51,820 ms.

The exponent has 36 bits. Both mlucas and mprime are limited to something below this. Can GPUs handle the trial factoring?

Dunno about GPU apps, but factor5 can handle it. I checked up to 74bits
already and no factors.

Your code above is up to ~66.6bits

? log(2*1000000000*58133053441+1)/log(2)
%1 = 66.655992491035654326600824278847640961

Edit: no factor to 2^75

[paulunderwood]

Originally Posted by hansl

Dunno about GPU apps, but factor5 can handle it. I checked up to 74bits
already and no factors.

Your code above is up to ~66.6bits

? log(2*1000000000*58133053441+1)/log(2)
%1 = 66.655992491035654326600824278847640961

Edit: no factor to 2^75

I am testing 76 to 77 bits

[hansl]

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

edit: No Factor from 75-76 bits.