Gratuitous factors thread

[fivemack]

This popped up on the Mersennus.net page and I managed to complete it in three real-time weeks on one machine (I'll admit it was an i9-7940X so quite a fast machine) - 2.5 days polynomial search, a bit of a gap while other jobs finished and I did the trial sieving, 12 days sieving, 1 day linear algebra.

32-bit LP, three algebraic large primes, alim=rlim=5e7, sieve Q=25M-75M (which is nice and round, but was determined by looking at yields incrementally rather than entirely in advance)

Notice how smooth the yield curve is when corrected for ideal count, and how the peak here is at alim. With this extra smoothness reasonable-sized trial sieving gives much more credible numbers; I'm not sure I'd have used 3lpa for things this small but it was clearly several percent better in the trial-sieve.

Expecting baby before next factor :)

[chris2be8]

Originally Posted by fivemack

Notice how smooth the yield curve is when corrected for ideal count

Can you confirm the ideal count is the first number on the following line output by gnfs-lasieve4I14e (in this case over a range of 10k special-Q):

522 Special q, 3933 reduction iterations

If that's true how many ideals should I assume per 10M special-Q? This would be a big help trial sieving numbers for NFS@Home.

Thanks in advance.

Chris

[charybdis]

Lucky ECM hit, from 3+2_1842M from the HCN tables:

GMP-ECM 7.0.5-dev [configured with GMP 6.2.0, --enable-asm-redc, --enable-assert] [ECM]
Input number is 2575167245145580345545358603140126953887375815021234731765984191692079396591260156613577262910448277094539273838808805370857935219624918675016962379584174887505043190773944811610010073257320929688633424357191886761888329736734042381290881 (238 digits)
Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=1:2166799276
Step 1 took 304804ms
Step 2 took 88190ms
********** Factor found in step 2: 1881941120468249708169539576246651193369513480043229827729929343069
Found prime factor of 67 digits: 1881941120468249708169539576246651193369513480043229827729929343069
Prime cofactor 1368356967780611326835948661781737382237519565564396399185048685206843247071058939238469661163518378115591947475004902031363212895011322108712962118435289831026432120434549 has 172 digits

[Happy5214]

This is (AFAIK) my personal ECM record:

122760214563986517403408012718327323026952918039831060056060998708807150488395908248657867219215800100789370303292314531669 = 85548851675281967428710863747045885644186850007163 * 1434972090916519038274518487801044320499147038941606461183097450445450863 (21^76:i208).

This P50 was found in just 410 curves at B1=3M. I lack patience and my hardware is really old, so this saved the sequence from exceeding the self-imposed C120 cofactor limit for NFS.

[unconnected]

Really lucky hit for aliquot sequence 79^91:i5

GMP-ECM 7.0.4 [configured with GMP 6.1.2, --enable-asm-redc] [ECM]
Input number is 265068640573758407535905984867282858553267450389668652958394878324092361572221738127508595352727313041526471350792042955118039583885472232715529 (144 digits)
...
Run 12 out of 150:
Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1:734709831
Step 1 took 143604ms
Step 2 took 52384ms
********** Factor found in step 2: 10622969779722833224233821696670456635150835905540542178233981211
Found prime factor of 65 digits: 10622969779722833224233821696670456635150835905540542178233981211
Prime cofactor 24952404654273090201857266161762430747111830388231810834477663075621591193735339 has 80 digits

It is my biggest ECM-factor so far. Previously I've several P63, P62, and P61 factors (none of them were found with B1>11e7 limit). Sadly even this record factor is not big enough to enter top10 yearly list.

[Stargate38]

P43 factor of C88 found by ecm.

ecm: 64/150 curves on C88, B1=250K, B2=gmp-ecm default, ETA: 21 sec
ecm: found prp43 factor = 2142249281864552971319672366351205960114907
ecm: 67/150 curves on C46, B1=250K, B2=gmp-ecm default, ETA: 21 sec
fac: setting target pretesting digits to 14.15
        t15: 51.14
        t20: 19.60
        t25: 2.39
        t30: 0.22
        t35: 0.02
fac: estimated sum of completed work is t26.11
fac: QS time estimation from tune data = 0.05 sec
fac: GNFS time estimation from tune data = 10.29 sec
pretesting / qs ratio was 4886.50
Total factoring time = 39.3250 seconds


***factors found***

P43 = 2142249281864552971319672366351205960114907
P46 = 1074732871675494834696515187318946620981020017

ans = 1

So far, that's my largest ECM find. I was very lucky to find it. From this sequence (i11)

[bsquared]

Originally Posted by Stargate38

P43 factor of C88 found by ecm.

ecm: 64/150 curves on C88, B1=250K, B2=gmp-ecm default, ETA: 21 sec
ecm: found prp43 factor = 2142249281864552971319672366351205960114907
ecm: 67/150 curves on C46, B1=250K, B2=gmp-ecm default, ETA: 21 sec
fac: setting target pretesting digits to 14.15
        t15: 51.14
        t20: 19.60
        t25: 2.39
        t30: 0.22
        t35: 0.02
fac: estimated sum of completed work is t26.11
fac: QS time estimation from tune data = 0.05 sec
fac: GNFS time estimation from tune data = 10.29 sec
pretesting / qs ratio was 4886.50
Total factoring time = 39.3250 seconds


***factors found***

P43 = 2142249281864552971319672366351205960114907
P46 = 1074732871675494834696515187318946620981020017

ans = 1

So far, that's my largest ECM find. I was very lucky to find it. From this sequence (i11)

Congrats, 64 curves @ B1=250k is super lucky. You'd expect to run over 500k curves before finding a 43 digit factor with B1=250k

[UBR47K]

Log:

Using B1=260000000-260000000, B2=3178559884516, polynomial Dickson(30), sigma=3:957017298
Step 1 took 0ms
Step 2 took 493313ms
********** Factor found in step 2: 15124628508282822860728592244514109925406256499230092227643
Found probable prime factor of 59 digits: 15124628508282822860728592244514109925406256499230092227643
Probable prime cofactor 4014473321008880083061629862535686360557015504856646058591888394131533153312046292751100693592725892009103700653633441678523812403799240000868489865492195879 has 157 digits

[sean]

Congratulations. For a moment I thought you had done the leading edge, but it is still nice to have this one done as well. So I see EM49 is now the smallest not completely factored number in this line (and EM52 of course).

[swishzzz]

Lucky find of the month:

Run 234 out of 800:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1:3420767960
Step 1 took 2265ms
Step 2 took 1438ms
********** Factor found in step 2: 76217327367748634991102091670295156034358967631469
Found prime factor of 50 digits: 76217327367748634991102091670295156034358967631469
Composite cofactor (10^199+6253)/76217327367748634991102091670295156034358967631469 has 150 digits

[kruoli]

Expected number of curves to find a factor of n digits:
35      40      45      50      55      60      65      70      75      80
1071    10283   118226  1565171 2.4e+07 3.9e+08 7.7e+09 2.9e+11 5.6e+16 7.6e+21

Not bad!