11113_235

Msieve v. 1.53 (SVN 1005)
Tue Nov 14 21:22:46 2023
random seeds: b0b124c8 263388a5
factoring 86247896883715999846072210793769813697130757540322594890616956504736978180171482312155465628665934135659962032232780835536890832299610331927930761859087 (152 digits)
searching for 15-digit factors
commencing number field sieve (152-digit input)
R0: -384722488742427811165352524196
R1: 4822283727213087671089
A0: -59959187481863067510154883369950343118
A1: 35977942110600584436551915397979
A2: 8593607460246613175475992
A3: -4225542010562443971
A4: -326105056170
A5: 25200
skew 5768867.69, size 9.533e-015, alpha -7.354, combined = 4.282e-012 rroots = 5

commencing relation filtering
setting target matrix density to 125.0
estimated available RAM is 16335.2 MB
commencing duplicate removal, pass 1
read 10M relations
error -9 reading relation 18251982
read 20M relations
error -1 reading relation 29717269
read 30M relations
read 40M relations
error -9 reading relation 47169130
read 50M relations
error -15 reading relation 55493430
read 60M relations
error -15 reading relation 62686801
error -9 reading relation 64220809
error -15 reading relation 66966793
read 70M relations
error -15 reading relation 73725458
error -15 reading relation 77471289
error -9 reading relation 77730959
read 80M relations
error -15 reading relation 88583699
read 90M relations
error -15 reading relation 93983232
read 100M relations
error -15 reading relation 109838171
read 110M relations
error -15 reading relation 110541066
error -9 reading relation 111486207
error -15 reading relation 112579455
error -1 reading relation 114605245
error -15 reading relation 115471848
error -1 reading relation 116169921
read 120M relations
error -1 reading relation 123897795
read 130M relations
read 140M relations
read 150M relations
read 160M relations
error -15 reading relation 162531576
error -9 reading relation 166022421
error -15 reading relation 166032188
skipped 4 relations with composite factors
found 22068795 hash collisions in 169848966 relations
added 121892 free relations
commencing duplicate removal, pass 2
found 18906383 duplicates and 151064475 unique relations
memory use: 788.8 MB
reading ideals above 51838976
commencing singleton removal, initial pass
memory use: 3012.0 MB
reading all ideals from disk
memory use: 2619.4 MB
commencing in-memory singleton removal
begin with 151064475 relations and 132069963 unique ideals
reduce to 81551200 relations and 54199918 ideals in 12 passes
max relations containing the same ideal: 28
reading ideals above 720000
commencing singleton removal, initial pass
memory use: 1506.0 MB
reading all ideals from disk
memory use: 2898.9 MB
keeping 59979304 ideals with weight <= 200, target excess is 432052
commencing in-memory singleton removal
begin with 81551200 relations and 59979304 unique ideals
reduce to 81550761 relations and 59978865 ideals in 4 passes
max relations containing the same ideal: 200
removing 8900656 relations and 6900656 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 72650105 relations and 59978865 unique ideals
reduce to 71927624 relations and 52333522 ideals in 9 passes
max relations containing the same ideal: 193
removing 6927810 relations and 4927810 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 64999814 relations and 52333522 unique ideals
reduce to 64502484 relations and 46894500 ideals in 7 passes
max relations containing the same ideal: 179
removing 6383708 relations and 4383708 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 58118776 relations and 46894500 unique ideals
reduce to 57681960 relations and 42061300 ideals in 7 passes
max relations containing the same ideal: 171
removing 6091442 relations and 4091442 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 51590518 relations and 42061300 unique ideals
reduce to 51174610 relations and 37540557 ideals in 6 passes
max relations containing the same ideal: 159
removing 5905822 relations and 3905822 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 45268788 relations and 37540557 unique ideals
reduce to 44854456 relations and 33205532 ideals in 6 passes
max relations containing the same ideal: 148
removing 5770395 relations and 3770395 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 39084061 relations and 33205532 unique ideals
reduce to 38656154 relations and 28990226 ideals in 7 passes
max relations containing the same ideal: 135
removing 5672198 relations and 3672198 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 32983956 relations and 28990226 unique ideals
reduce to 32526143 relations and 24839479 ideals in 6 passes
max relations containing the same ideal: 121
removing 5595663 relations and 3595663 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 26930480 relations and 24839479 unique ideals
reduce to 26420765 relations and 20707360 ideals in 7 passes
max relations containing the same ideal: 106
removing 5543072 relations and 3543072 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 20877693 relations and 20707360 unique ideals
reduce to 20284377 relations and 16532712 ideals in 8 passes
max relations containing the same ideal: 86
removing 5491520 relations and 3491520 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 14792857 relations and 16532712 unique ideals
reduce to 14050764 relations and 12236654 ideals in 7 passes
max relations containing the same ideal: 68
removing 3804484 relations and 2491555 ideals in 1312929 cliques
commencing in-memory singleton removal
begin with 10246280 relations and 12236654 unique ideals
reduce to 9662599 relations and 9112440 ideals in 8 passes
max relations containing the same ideal: 51
removing 266764 relations and 217786 ideals in 48978 cliques
commencing in-memory singleton removal
begin with 9395835 relations and 9112440 unique ideals
reduce to 9390419 relations and 8889210 ideals in 6 passes
max relations containing the same ideal: 51
relations with 0 large ideals: 1358
relations with 1 large ideals: 12282
relations with 2 large ideals: 153794
relations with 3 large ideals: 760529
relations with 4 large ideals: 1898039
relations with 5 large ideals: 2670239
relations with 6 large ideals: 2269614
relations with 7+ large ideals: 1624564
commencing 2-way merge
reduce to 5960432 relation sets and 5459223 unique ideals
commencing full merge
memory use: 726.9 MB
found 2733341 cycles, need 2689423
weight of 2689423 cycles is about 336389621 (125.08/cycle)
distribution of cycle lengths:
1 relations: 56708
2 relations: 130975
3 relations: 173208
4 relations: 191408
5 relations: 205808
6 relations: 210287
7 relations: 209233
8 relations: 202144
9 relations: 189493
10+ relations: 1120159
heaviest cycle: 28 relations
commencing cycle optimization
start with 24526217 relations
pruned 1218296 relations
memory use: 638.8 MB
distribution of cycle lengths:
1 relations: 56708
2 relations: 134834
3 relations: 181249
4 relations: 200382
5 relations: 218071
6 relations: 222859
7 relations: 222536
8 relations: 214007
9 relations: 199867
10+ relations: 1038910
heaviest cycle: 26 relations
RelProcTime: 4127

commencing linear algebra
read 2689423 cycles
cycles contain 9139459 unique relations
read 9139459 relations
using 20 quadratic characters above 4294917295
building initial matrix
memory use: 1271.2 MB
read 2689423 cycles
matrix is 2689244 x 2689423 (1295.0 MB) with weight 394039921 (146.51/col)
sparse part has weight 309903030 (115.23/col)
filtering completed in 2 passes
matrix is 2689152 x 2689331 (1295.0 MB) with weight 394034247 (146.52/col)
sparse part has weight 309900355 (115.23/col)
matrix starts at (0, 0)
matrix is 2689152 x 2689331 (1295.0 MB) with weight 394034247 (146.52/col)
sparse part has weight 309900355 (115.23/col)
saving the first 48 matrix rows for later
matrix includes 64 packed rows
matrix is 2689104 x 2689331 (1262.7 MB) with weight 339436371 (126.22/col)
sparse part has weight 304113597 (113.08/col)
using block size 8192 and superblock size 589824 for processor cache size 6144 kB
commencing Lanczos iteration (4 threads)
memory use: 1031.3 MB
linear algebra at 0.1%, ETA 3h56m2689331 dimensions (0.1%, ETA 3h56m)
checkpointing every 670000 dimensions331 dimensions (0.1%, ETA 4h 4m)
linear algebra completed 2688994 of 2689331 dimensions (100.0%, ETA 0h 0m)
lanczos halted after 42527 iterations (dim = 2689102)
recovered 29 nontrivial dependencies
BLanczosTime: 14407

commencing square root phase
handling dependencies 1 to 64
reading relations for dependency 1
read 1343909 cycles
cycles contain 4569384 unique relations
read 4569384 relations
multiplying 4569384 relations
multiply complete, coefficients have about 231.27 million bits
initial square root is modulo 199313077
sqrtTime: 834
p71 factor: 42318799738888422270866190369454644519405196167708792848664830252528189
p82 factor: 2038051585013631405010146550877038692378441678342743215720427536637829215296154683
elapsed time 05:22:49