M2629093 has a factor: 63721413359381377

[James Heinrich]

M2629093 has a factor: 63721413359381377

I found this, unexpectedly, in P-1 stage2. The question is, why wasn't it found before? As far as PrimeNet knew, it was TF'd up to 2^61 (unfortunately, PrimeNet erases, or at least doesn't display, other details of an exponent's history once a factor is found), and this should've been found in TF to 2^56 (mfaktc also found the factor no problem when I asked it to look in that range). So how was it skipped on PrimeNet? Faked results?

[lycorn]

TF ro 61 bits performed by a faulty machine?

[cheesehead]

How long would it take for a 64-bit system to do a TF to 2^56 on all unfactored exponents up to, say, 50M?

[James Heinrich]

Originally Posted by cheesehead

How long would it take for a 64-bit system to do a TF to 2^56 on all unfactored exponents up to, say, 50M?

In terms of actual work (note that effort numbers are culmulative, not per-range):

up to M1,xxx,xxx = 508GHz-days
up to M2,xxx,xxx = 638GHz-days
up to M3,xxx,xxx = 726GHz-days
up to M4,xxx,xxx = 792GHz-days
up to M5,xxx,xxx = 842GHz-days
up to M6,xxx,xxx = 882GHz-days
up to M7,xxx,xxx = 914GHz-days
up to M8,xxx,xxx = 944GHz-days
up to M9,xxx,xxx = 970GHz-days
up to M10,xxx,xxx = 993GHz-days
up to M11,xxx,xxx = 1,014GHz-days
up to M12,xxx,xxx = 1,033GHz-days
up to M13,xxx,xxx = 1,051GHz-days
up to M14,xxx,xxx = 1,067GHz-days
up to M15,xxx,xxx = 1,082GHz-days
up to M16,xxx,xxx = 1,096GHz-days
up to M17,xxx,xxx = 1,109GHz-days
up to M18,xxx,xxx = 1,121GHz-days
up to M19,xxx,xxx = 1,133GHz-days
up to M20,xxx,xxx = 1,144GHz-days
up to M21,xxx,xxx = 1,154GHz-days
up to M22,xxx,xxx = 1,164GHz-days
up to M23,xxx,xxx = 1,173GHz-days
up to M24,xxx,xxx = 1,182GHz-days
up to M25,xxx,xxx = 1,191GHz-days
up to M26,xxx,xxx = 1,199GHz-days
up to M27,xxx,xxx = 1,207GHz-days
up to M28,xxx,xxx = 1,214GHz-days
up to M29,xxx,xxx = 1,222GHz-days
up to M30,xxx,xxx = 1,229GHz-days
up to M31,xxx,xxx = 1,236GHz-days
up to M32,xxx,xxx = 1,242GHz-days
up to M33,xxx,xxx = 1,248GHz-days
up to M34,xxx,xxx = 1,255GHz-days
up to M35,xxx,xxx = 1,261GHz-days
up to M36,xxx,xxx = 1,266GHz-days
up to M37,xxx,xxx = 1,272GHz-days
up to M38,xxx,xxx = 1,277GHz-days
up to M39,xxx,xxx = 1,283GHz-days
up to M40,xxx,xxx = 1,288GHz-days
up to M41,xxx,xxx = 1,293GHz-days
up to M42,xxx,xxx = 1,298GHz-days
up to M43,xxx,xxx = 1,303GHz-days
up to M44,xxx,xxx = 1,307GHz-days
up to M45,xxx,xxx = 1,312GHz-days
up to M46,xxx,xxx = 1,317GHz-days
up to M47,xxx,xxx = 1,321GHz-days
up to M48,xxx,xxx = 1,325GHz-days
up to M49,xxx,xxx = 1,329GHz-days

Note that the amount of effort to factor to a fixed bitdepth varies greatly on the exponent size (smaller exponents, lots more effort).

A variant approach would be to TF to 4 bitlevels below the default level for that range, which yields very different numbers:

up to M1,xxx,xxx = 0GHz-days (~2^52)
up to M2,xxx,xxx = 13GHz-days (~2^54)
up to M3,xxx,xxx = 50GHz-days (~2^56)
up to M4,xxx,xxx = 118GHz-days (~2^57)
up to M5,xxx,xxx = 218GHz-days (~2^57)
up to M6,xxx,xxx = 361GHz-days (~2^58)
up to M7,xxx,xxx = 490GHz-days (~2^59)
up to M8,xxx,xxx = 608GHz-days (~2^59)
up to M9,xxx,xxx = 789GHz-days (~2^60)
up to M10,xxx,xxx = 975GHz-days (~2^60)
up to M11,xxx,xxx = 1,144GHz-days (~2^60)
up to M12,xxx,xxx = 1,297GHz-days (~2^60)
up to M13,xxx,xxx = 1,439GHz-days (~2^60)
up to M14,xxx,xxx = 1,647GHz-days (~2^61)
up to M15,xxx,xxx = 1,886GHz-days (~2^61)
up to M16,xxx,xxx = 2,112GHz-days (~2^61)
up to M17,xxx,xxx = 2,322GHz-days (~2^61)
up to M18,xxx,xxx = 2,518GHz-days (~2^61)
up to M19,xxx,xxx = 2,703GHz-days (~2^61)
up to M20,xxx,xxx = 2,876GHz-days (~2^61)
up to M21,xxx,xxx = 3,041GHz-days (~2^61)
up to M22,xxx,xxx = 3,199GHz-days (~2^61)
up to M23,xxx,xxx = 3,347GHz-days (~2^61)
up to M24,xxx,xxx = 3,574GHz-days (~2^62)
up to M25,xxx,xxx = 3,848GHz-days (~2^62)
up to M26,xxx,xxx = 4,109GHz-days (~2^62)
up to M27,xxx,xxx = 4,364GHz-days (~2^62)
up to M28,xxx,xxx = 4,608GHz-days (~2^62)
up to M29,xxx,xxx = 4,841GHz-days (~2^62)
up to M30,xxx,xxx = 5,219GHz-days (~2^63)
up to M31,xxx,xxx = 5,918GHz-days (~2^63)
up to M32,xxx,xxx = 6,593GHz-days (~2^63)
up to M33,xxx,xxx = 7,244GHz-days (~2^63)
up to M34,xxx,xxx = 7,867GHz-days (~2^63)
up to M35,xxx,xxx = 8,481GHz-days (~2^63)
up to M36,xxx,xxx = 9,075GHz-days (~2^63)
up to M37,xxx,xxx = 9,647GHz-days (~2^63)
up to M38,xxx,xxx = 10,313GHz-days (~2^64)
up to M39,xxx,xxx = 11,403GHz-days (~2^64)
up to M40,xxx,xxx = 12,462GHz-days (~2^64)
up to M41,xxx,xxx = 13,500GHz-days (~2^64)
up to M42,xxx,xxx = 14,510GHz-days (~2^64)
up to M43,xxx,xxx = 15,492GHz-days (~2^64)
up to M44,xxx,xxx = 16,460GHz-days (~2^64)
up to M45,xxx,xxx = 17,387GHz-days (~2^64)
up to M46,xxx,xxx = 18,304GHz-days (~2^64)
up to M47,xxx,xxx = 19,201GHz-days (~2^64)
up to M48,xxx,xxx = 20,507GHz-days (~2^65)
up to M49,xxx,xxx = 22,139GHz-days (~2^65)
up to M50,xxx,xxx = 23,737GHz-days (~2^65)

Or for 8 levels below standard:

up to M1,xxx,xxx = 0GHz-days (~2^48)
up to M2,xxx,xxx = 1GHz-days (~2^50)
up to M3,xxx,xxx = 3GHz-days (~2^52)
up to M4,xxx,xxx = 7GHz-days (~2^53)
up to M5,xxx,xxx = 14GHz-days (~2^53)
up to M6,xxx,xxx = 23GHz-days (~2^54)
up to M7,xxx,xxx = 34GHz-days (~2^55)
up to M8,xxx,xxx = 49GHz-days (~2^55)
up to M9,xxx,xxx = 71GHz-days (~2^56)
up to M10,xxx,xxx = 95GHz-days (~2^56)
up to M11,xxx,xxx = 116GHz-days (~2^56)
up to M12,xxx,xxx = 135GHz-days (~2^56)
up to M13,xxx,xxx = 153GHz-days (~2^56)
up to M14,xxx,xxx = 179GHz-days (~2^57)
up to M15,xxx,xxx = 209GHz-days (~2^57)
up to M16,xxx,xxx = 237GHz-days (~2^57)
up to M17,xxx,xxx = 263GHz-days (~2^57)
up to M18,xxx,xxx = 288GHz-days (~2^57)
up to M19,xxx,xxx = 311GHz-days (~2^57)
up to M20,xxx,xxx = 332GHz-days (~2^57)
up to M21,xxx,xxx = 353GHz-days (~2^57)
up to M22,xxx,xxx = 373GHz-days (~2^57)
up to M23,xxx,xxx = 391GHz-days (~2^57)
up to M24,xxx,xxx = 420GHz-days (~2^58)
up to M25,xxx,xxx = 454GHz-days (~2^58)
up to M26,xxx,xxx = 486GHz-days (~2^58)
up to M27,xxx,xxx = 518GHz-days (~2^58)
up to M28,xxx,xxx = 549GHz-days (~2^58)
up to M29,xxx,xxx = 578GHz-days (~2^58)
up to M30,xxx,xxx = 606GHz-days (~2^59)
up to M31,xxx,xxx = 633GHz-days (~2^59)
up to M32,xxx,xxx = 660GHz-days (~2^59)
up to M33,xxx,xxx = 685GHz-days (~2^59)
up to M34,xxx,xxx = 710GHz-days (~2^59)
up to M35,xxx,xxx = 734GHz-days (~2^59)
up to M36,xxx,xxx = 757GHz-days (~2^59)
up to M37,xxx,xxx = 779GHz-days (~2^59)
up to M38,xxx,xxx = 805GHz-days (~2^60)
up to M39,xxx,xxx = 848GHz-days (~2^60)
up to M40,xxx,xxx = 889GHz-days (~2^60)
up to M41,xxx,xxx = 930GHz-days (~2^60)
up to M42,xxx,xxx = 969GHz-days (~2^60)
up to M43,xxx,xxx = 1,008GHz-days (~2^60)
up to M44,xxx,xxx = 1,046GHz-days (~2^60)
up to M45,xxx,xxx = 1,082GHz-days (~2^60)
up to M46,xxx,xxx = 1,118GHz-days (~2^60)
up to M47,xxx,xxx = 1,153GHz-days (~2^60)
up to M48,xxx,xxx = 1,206GHz-days (~2^61)
up to M49,xxx,xxx = 1,273GHz-days (~2^61)
up to M50,xxx,xxx = 1,339GHz-days (~2^61)

Or for the lesser of (default TF level -or- 2^56):

up to M1,xxx,xxx = 0GHz-days (~2^52)
up to M2,xxx,xxx = 13GHz-days (~2^54)
up to M3,xxx,xxx = 50GHz-days (~2^56)
up to M4,xxx,xxx = 116GHz-days (~2^56)
up to M5,xxx,xxx = 166GHz-days (~2^56)
up to M6,xxx,xxx = 205GHz-days (~2^56)
up to M7,xxx,xxx = 237GHz-days (~2^56)
up to M8,xxx,xxx = 267GHz-days (~2^56)
up to M9,xxx,xxx = 293GHz-days (~2^56)
up to M10,xxx,xxx = 316GHz-days (~2^56)
up to M11,xxx,xxx = 337GHz-days (~2^56)
up to M12,xxx,xxx = 356GHz-days (~2^56)
up to M13,xxx,xxx = 374GHz-days (~2^56)
up to M14,xxx,xxx = 390GHz-days (~2^56)
up to M15,xxx,xxx = 405GHz-days (~2^56)
up to M16,xxx,xxx = 419GHz-days (~2^56)
up to M17,xxx,xxx = 432GHz-days (~2^56)
up to M18,xxx,xxx = 445GHz-days (~2^56)
up to M19,xxx,xxx = 456GHz-days (~2^56)
up to M20,xxx,xxx = 467GHz-days (~2^56)
up to M21,xxx,xxx = 477GHz-days (~2^56)
up to M22,xxx,xxx = 487GHz-days (~2^56)
up to M23,xxx,xxx = 497GHz-days (~2^56)
up to M24,xxx,xxx = 505GHz-days (~2^56)
up to M25,xxx,xxx = 514GHz-days (~2^56)
up to M26,xxx,xxx = 522GHz-days (~2^56)
up to M27,xxx,xxx = 530GHz-days (~2^56)
up to M28,xxx,xxx = 538GHz-days (~2^56)
up to M29,xxx,xxx = 545GHz-days (~2^56)
up to M30,xxx,xxx = 552GHz-days (~2^56)
up to M31,xxx,xxx = 559GHz-days (~2^56)
up to M32,xxx,xxx = 565GHz-days (~2^56)
up to M33,xxx,xxx = 572GHz-days (~2^56)
up to M34,xxx,xxx = 578GHz-days (~2^56)
up to M35,xxx,xxx = 584GHz-days (~2^56)
up to M36,xxx,xxx = 590GHz-days (~2^56)
up to M37,xxx,xxx = 595GHz-days (~2^56)
up to M38,xxx,xxx = 601GHz-days (~2^56)
up to M39,xxx,xxx = 606GHz-days (~2^56)
up to M40,xxx,xxx = 611GHz-days (~2^56)
up to M41,xxx,xxx = 616GHz-days (~2^56)
up to M42,xxx,xxx = 621GHz-days (~2^56)
up to M43,xxx,xxx = 626GHz-days (~2^56)
up to M44,xxx,xxx = 631GHz-days (~2^56)
up to M45,xxx,xxx = 635GHz-days (~2^56)
up to M46,xxx,xxx = 640GHz-days (~2^56)
up to M47,xxx,xxx = 644GHz-days (~2^56)
up to M48,xxx,xxx = 648GHz-days (~2^56)
up to M49,xxx,xxx = 653GHz-days (~2^56)
up to M50,xxx,xxx = 657GHz-days (~2^65)

Assuming a 4-core i7-920 @ 3.0GHz can do 4.6GHz-days per day per core, it can do approx 560GHz-days per month of TF. You can figure out how long it would take to do any/all of the above.
edit: of course, a system with a good CUDA GPU could potentially get it done much faster...

[Uncwilly]

Originally Posted by cheesehead

How long would it take for a 64-bit system to do a TF to 2^56 on all unfactored exponents up to, say, 50M?

Maybe someone with a hot GPU and mfaktc could do this as a project (at least in part.)

[James Heinrich]

Originally Posted by Uncwilly

Maybe someone with a hot GPU and mfaktc could do this as a project (at least in part.)

I could generate the big worktodo if anyone wants to take it on.
<a few minutes pass>
Actually, I did, so people can grab it and work on it if they want. But someone should co-ordinate the effort so there's not too much overlap of work. There's just over 1 million assignment lines :surprised
http://mersenne-aries.sili.net/temp/worktodo-TF56.7z (since attachments here are limited to 256kB)

[firejuggler]

don't forget that mfaktc ignore the exponent below 1 000 000

[KingKurly]

Originally Posted by James Heinrich

I could generate the big worktodo if anyone wants to take it on.
<a few minutes pass>
Actually, I did, so people can grab it and work on it if they want. But someone should co-ordinate the effort so there's not too much overlap of work. There's just over 1 million assignment lines :surprised
http://mersenne-aries.sili.net/temp/worktodo-TF56.7z (since attachments here are limited to 256kB)

I did M4999XXXX and found nothing (...which, I suppose, is exactly what I expected to find!) Even though it took barely any time at all, I don't plan on continuing unless I come across some spare CPU/GPU time. I've already got enough assignments, and every time I look at your P1small page I always find more...

I wonder how many factors we should expect to find, if someone decides to continue (start?) the effort. I mean, sure, we shouldn't find any, but I think the point of the exercise is that we may well find some missing ones.

[firejuggler]

ok so...
gtx 460 and core 2 duo E8300.
one assignement take about 18 seconds. but use 'only' 60 M/sec . It goes up to 120 M/s on billion digit assignment under full load.
but since I only have 2 core, it slow down a bit.... so with 2 instance, i get one assignment in 21 seconds, plus half of one between the end of one and the start of the following.

Considering 1 M assignment, 21 500 000 seconds/2=10 750 000, 10750000/3600,2986.1 hours or a bit more than 124 days of work.

[James Heinrich]

Originally Posted by firejuggler

don't forget that mfaktc ignore the exponent below 1 000 000

And likewise Prime95 refuses TF on exponents < 20,000

[James Heinrich]

Since I don't have a particularly good GPU to throw at it, I'll just run the ~14000 exponents <1M overnight (on Prime95) and see what it comes up with. I'm churning through them at about 1/second in that range, so shouldn't take long. Hopefully no factors ;)