92228_246

Msieve v. 1.53 (SVN 1005)
Tue Jul 18 10:37:04 2023
random seeds: 541db8f0 68b63233
factoring 4198924236247233616318339717301335789910619603174450035718483306514696383674698298593565783348830649578279197255133502656041104844523613621302493 (145 digits)
searching for 15-digit factors
commencing number field sieve (145-digit input)
R0: -10229291208461590107351406186
R1: 658448796960779657179
A0: 3111317225842969928040666666373410
A1: -14398789290158606610969567175
A2: -53716294930765355878932
A3: 117504807639652291
A4: 346706119536
A5: 876960
skew 353572.67, size 4.820e-014, alpha -6.709, combined = 1.111e-011 rroots = 3

commencing relation filtering
setting target matrix density to 110.0
estimated available RAM is 16335.2 MB
commencing duplicate removal, pass 1
error -9 reading relation 4571304
error -5 reading relation 6934907
error -9 reading relation 9892756
read 10M relations
read 20M relations
read 30M relations
error -15 reading relation 36810393
read 40M relations
read 50M relations
error -15 reading relation 54020988
error -15 reading relation 55543474
read 60M relations
read 70M relations
read 80M relations
read 90M relations
error -1 reading relation 94333428
read 100M relations
error -15 reading relation 105677717
error -9 reading relation 107661378
read 110M relations
error -9 reading relation 111012174
error -15 reading relation 111324789
skipped 4 relations with composite factors
found 17301653 hash collisions in 111351007 relations
added 121181 free relations
commencing duplicate removal, pass 2
found 15062647 duplicates and 96409541 unique relations
memory use: 660.8 MB
reading ideals above 41091072
commencing singleton removal, initial pass
memory use: 1506.0 MB
reading all ideals from disk
memory use: 1576.3 MB
commencing in-memory singleton removal
begin with 96409541 relations and 70783128 unique ideals
reduce to 63788857 relations and 35380317 ideals in 10 passes
max relations containing the same ideal: 33
reading ideals above 720000
commencing singleton removal, initial pass
memory use: 753.0 MB
reading all ideals from disk
memory use: 2188.0 MB
keeping 40025820 ideals with weight <= 200, target excess is 342654
commencing in-memory singleton removal
begin with 63788857 relations and 40025820 unique ideals
reduce to 63788797 relations and 40025760 ideals in 4 passes
max relations containing the same ideal: 200
removing 6098665 relations and 4098665 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 57690132 relations and 40025760 unique ideals
reduce to 57265804 relations and 35486296 ideals in 6 passes
max relations containing the same ideal: 195
removing 5202928 relations and 3202928 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 52062876 relations and 35486296 unique ideals
reduce to 51796858 relations and 32008075 ideals in 6 passes
max relations containing the same ideal: 185
removing 4953700 relations and 2953700 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 46843158 relations and 32008075 unique ideals
reduce to 46625707 relations and 28829411 ideals in 5 passes
max relations containing the same ideal: 174
removing 4800526 relations and 2800526 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 41825181 relations and 28829411 unique ideals
reduce to 41630156 relations and 25826750 ideals in 5 passes
max relations containing the same ideal: 161
removing 4690112 relations and 2690112 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 36940044 relations and 25826750 unique ideals
reduce to 36757378 relations and 22947121 ideals in 6 passes
max relations containing the same ideal: 150
removing 4599352 relations and 2599352 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 32158026 relations and 22947121 unique ideals
reduce to 31981057 relations and 20163950 ideals in 5 passes
max relations containing the same ideal: 139
removing 4517433 relations and 2517433 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 27463624 relations and 20163950 unique ideals
reduce to 27287512 relations and 17463097 ideals in 5 passes
max relations containing the same ideal: 122
removing 4443162 relations and 2443162 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 22844350 relations and 17463097 unique ideals
reduce to 22659798 relations and 14827351 ideals in 6 passes
max relations containing the same ideal: 107
removing 4372509 relations and 2372509 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 18287289 relations and 14827351 unique ideals
reduce to 18089652 relations and 12247885 ideals in 6 passes
max relations containing the same ideal: 95
removing 4299550 relations and 2299550 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 13790102 relations and 12247885 unique ideals
reduce to 13580853 relations and 9728520 ideals in 6 passes
max relations containing the same ideal: 76
removing 2938339 relations and 1569205 ideals in 1369134 cliques
commencing in-memory singleton removal
begin with 10642514 relations and 9728520 unique ideals
reduce to 10441307 relations and 7947594 ideals in 6 passes
max relations containing the same ideal: 61
removing 2080283 relations and 1132698 ideals in 947585 cliques
commencing in-memory singleton removal
begin with 8361024 relations and 7947594 unique ideals
reduce to 8149166 relations and 6590472 ideals in 6 passes
max relations containing the same ideal: 55
removing 1870055 relations and 1033712 ideals in 836343 cliques
commencing in-memory singleton removal
begin with 6279111 relations and 6590472 unique ideals
reduce to 6040307 relations and 5301342 ideals in 8 passes
max relations containing the same ideal: 46
removing 881623 relations and 540137 ideals in 341486 cliques
commencing in-memory singleton removal
begin with 5158684 relations and 5301342 unique ideals
reduce to 5021562 relations and 4616556 ideals in 7 passes
max relations containing the same ideal: 43
relations with 0 large ideals: 1069
relations with 1 large ideals: 15227
relations with 2 large ideals: 133095
relations with 3 large ideals: 516061
relations with 4 large ideals: 1096328
relations with 5 large ideals: 1396344
relations with 6 large ideals: 1113849
relations with 7+ large ideals: 749589
commencing 2-way merge
reduce to 4020759 relation sets and 3615753 unique ideals
commencing full merge
memory use: 414.5 MB
found 1729624 cycles, need 1685953
weight of 1685953 cycles is about 186201397 (110.44/cycle)
distribution of cycle lengths:
1 relations: 48618
2 relations: 109869
3 relations: 139839
4 relations: 145609
5 relations: 148600
6 relations: 141214
7 relations: 133544
8 relations: 122292
9 relations: 110527
10+ relations: 585841
heaviest cycle: 25 relations
commencing cycle optimization
start with 13832000 relations
pruned 955335 relations
memory use: 345.5 MB
distribution of cycle lengths:
1 relations: 48618
2 relations: 114775
3 relations: 150411
4 relations: 157369
5 relations: 162037
6 relations: 152948
7 relations: 144394
8 relations: 129859
9 relations: 116247
10+ relations: 509295
heaviest cycle: 25 relations
RelProcTime: 2875

commencing linear algebra
read 1685953 cycles
cycles contain 4821177 unique relations
read 4821177 relations
using 20 quadratic characters above 4294917295
building initial matrix
memory use: 691.8 MB
read 1685953 cycles
matrix is 1685768 x 1685953 (717.7 MB) with weight 224260179 (133.02/col)
sparse part has weight 167920076 (99.60/col)
filtering completed in 2 passes
matrix is 1685404 x 1685589 (717.7 MB) with weight 224234600 (133.03/col)
sparse part has weight 167907167 (99.61/col)
matrix starts at (0, 0)
matrix is 1685404 x 1685589 (717.7 MB) with weight 224234600 (133.03/col)
sparse part has weight 167907167 (99.61/col)
saving the first 48 matrix rows for later
matrix includes 64 packed rows
matrix is 1685356 x 1685589 (698.6 MB) with weight 187955482 (111.51/col)
sparse part has weight 166271317 (98.64/col)
using block size 8192 and superblock size 589824 for processor cache size 6144 kB
commencing Lanczos iteration (4 threads)
memory use: 563.8 MB
linear algebra at 0.1%, ETA 1h32m1685589 dimensions (0.1%, ETA 1h32m)
checkpointing every 1040000 dimensions89 dimensions (0.1%, ETA 1h37m)
linear algebra completed 1685348 of 1685589 dimensions (100.0%, ETA 0h 0m)
lanczos halted after 26650 iterations (dim = 1685355)
recovered 32 nontrivial dependencies
BLanczosTime: 5914

commencing square root phase
handling dependencies 1 to 64
reading relations for dependency 1
read 842699 cycles
cycles contain 2411066 unique relations
read 2411066 relations
multiplying 2411066 relations
multiply complete, coefficients have about 127.97 million bits
initial square root is modulo 1533383653
GCD is 1, no factor found
reading relations for dependency 2
read 842970 cycles
cycles contain 2409736 unique relations
read 2409736 relations
multiplying 2409736 relations
multiply complete, coefficients have about 127.91 million bits
initial square root is modulo 1515967471
sqrtTime: 738
p59 factor: 48140301026202126109058277083398478724390981663136730025461
p86 factor: 87222641876747196788374508733653748607018288342676960232211701242879123883785881981513
elapsed time 02:38:48