That's... an incredible string of luck, is it not?

[QUOTE=Dubslow;470255]
Not coincidentally, I would like to reserve 37061^43-1 to factor. (I have a 6 year old quad core only, so small numbers for me! Even this will probably take more than a month.)[/QUOTE]

Evidently my memory fails me. ~3 days, though I perhaps got slightly unlucky with the ECM: Yafu found the P45, but not the P42 or P43, and thus switched to SNFS and probably overall wasted time... but hindsight is in this case 40/20.

[code]P45 = 151391679468422393528867290915149240097250107
P64 = 1486558991225034419006760671754467301035250060013637466479042797
P43 = 7085347601112630074165665314424610195957819
P42 = 491910406011895000965792057486858753525323
[/code]

I'll take the next three smallest available:

5366319547249^17-1
671717139553^19-1
24671431560073^17-1

[QUOTE=Dubslow;470379]That's... an incredible string of luck, is it not?[/QUOTE]

It's not that lucky. I'm factoring about half of them by ECM, so 3 in a row is a 1 in 8 chance.

Chris

[QUOTE=chris2be8;470389]It's not that lucky. I'm factoring about half of them by ECM[/QUOTE]

Really? I didn't realize the pickings were quite that good. What's the smallest factors you see? 20 digits, 30, 35?

[QUOTE=Dubslow;470387]I'll take the next three smallest available:

5366319547249^17-1 # SNFS diff: 254.593, degree 6, GNFS diff: 203.675, CPU hours: 21607, weight: 17609, ratio 0.814961120629172
671717139553^19-1 # SNFS diff: 248.370, degree 6, GNFS diff: 212.889, CPU hours: 13379, weight: 11396, ratio 0.851726491726239
24671431560073^17-1 # SNFS diff: 267.843, degree 6, GNFS diff: 214.275, CPU hours: 59948, weight: 30973, ratio 0.516657121787173 [/QUOTE]

Those are a lot harder. I've added SNFS difficulty and CPU hours etc estimated by my script to your post. Compare with:
37061^43-1 # SNFS diff: 207.601, degree 6, GNFS diff: 191.895, CPU hours: 579.188, weight: 7664, ratio 13.2323092955755

So if that took 3 days you are doing the equivalent of about 200 CPU hours per day. So the next 3 might take you 100 days, 66 days and 300 days respectively. They are probably more suited to NFS@Home.

In practice I'm not planning to do any more myself.

Chris

[QUOTE=Dubslow;470392]Really? I didn't realize the pickings were quite that good. What's the smallest factors you see? 20 digits, 30, 35?[/QUOTE]

I've posted nearly all the ECM factors I found to this list (mainly to show why I was reserving another number so quickly). The smallest factor was 34 digits.

I'm using my GPU to do stage 1 so ECM is quite fast for me.

Chris

[QUOTE=chris2be8;470393]Those are a lot harder. I've added SNFS difficulty and CPU hours etc estimated by my script to your post. Compare with:
37061^43-1 # SNFS diff: 207.601, degree 6, GNFS diff: 191.895, CPU hours: 579.188, weight: 7664, ratio 13.2323092955755

So if that took 3 days you are doing the equivalent of about 200 CPU hours per day. So the next 3 might take you 100 days, 66 days and 300 days respectively. They are probably more suited to NFS@Home.

In practice I'm not planning to do any more myself.

Chris[/QUOTE]

Aww crud. First order SNFS difficulty estimation: smote. I'm rusty on my SNFS techniques, but this is because of the relatively large base? Especially for the 17s, multiplying by one factor of the base to get the degree 6 poly is a significant penalty.

But actually, for the middle one, shouldn't it be doable with a degree 6 without any penalty multiplications? Something like c6=671717139553, c0=-1, m=671717139553^3, and the difficulty stays at merely the size of the composite? What am I forgetting?

I've checked what my script does, it adds a penalty to the SNFS difficulty for the large coefficients so the estimated CPU time isn't too far out. So the SNFS difficulty is smaller that it says. But the CPU time is probably about right.

I should fix it to print the real SNFS difficulty, then adjust it before calculating CPU time. But that's really a cosmetic fix.

If you want to do them do some test sieving to get a better estimate of how long they will take.

Sorting by estimated CPU time the next three would be:
(65551^47-1)/65550
(21377^53-1)/21376
(47306791574323349111302419726723197703462364929251918941^5-1)/2601873536587784201121633084969775873690430071108855541700

Those would be at the small end of jobs for NFS@Home. So feasible for 1 system if you are willing to take a few weeks for each of them.

Chris

[QUOTE=chris2be8;470398]I've checked what my script does, it adds a penalty to the SNFS difficulty for the large coefficients so the estimated CPU time isn't too far out. So the SNFS difficulty is smaller that it says. But the CPU time is probably about right.

I should fix it to print the real SNFS difficulty, then adjust it before calculating CPU time. But that's really a cosmetic fix.

If you want to do them do some test sieving to get a better estimate of how long they will take.

Sorting by estimated CPU time the next three would be:
(65551^47-1)/65550
(21377^53-1)/21376
(47306791574323349111302419726723197703462364929251918941^5-1)/2601873536587784201121633084969775873690430071108855541700

Those would be at the small end of jobs for NFS@Home. So feasible for 1 system if you are willing to take a few weeks for each of them.

Chris[/QUOTE]

In fact I've already pushed the 473xx941^5-1 to the NFS@home 15e queue. As you can see from the Q range these are small jobs for 15e, but the yield-per-second is much higher for 15e than for 14e.

The middle one looks entirely practical, with the obvious SNFS polynomial and unoptimised parameters below I get a yield with 15e at Q=134M of 4.806 rel/Q and a runtime of 0.12s/rel on one core 2.5GHz Ivy Bridge, so maybe 12000 CPU-hours sieving to get enough relations for a matrix.

(oh, I'm an idiot and was looking in the wrong column, that's pretty much the same estimate that Chris has! also I have enough cores for 10,000 CPU-hours per week)

(my guess is that the Murphy E-value computed by msieve will be closely correlated to the sieving yield and the runtime; it might be a more useful figure of merit than 'SNFS digits')

[code]
n: 775096433203518536044933353171710557475540401430117459326084334844306873036759431760612632327979348785118615047871598479663542525065118826315208419605410714190495159843711804117366552926395923017505967925465157683
skew: 93.583
c0: 671717139553
c6: -1
Y0: -1
Y1: 303081403521299656161314946389465377
lpbr: 32
lpba: 32
mfbr: 64
mfba: 64
alambda: 2.6
rlambda: 2.6
alim: 134000000
rlim: 134000000

[/code]

How much ECM has been done on (732541^47-1)/732540 ?