21119_225

Msieve v. 1.53 (SVN 1005)
Thu Nov 09 07:03:41 2023
random seeds: 2f75be5c 85520a8f
factoring 4902737470322779045000095205942834188952916417389623425279633694873746841005867517231949073013927523377246675748351267765713332464954229993980167966869 (151 digits)
searching for 15-digit factors
commencing number field sieve (151-digit input)
R0: -103343246984629313758552958652
R1: 24364837955404017980393
A0: 57994586801399960788010844644007783
A1: 522671367722987729718103530429
A2: -2695261296203260798804903
A3: -4198390204866137699
A4: 4668602337750
A5: 5405400
skew 604214.48, size 1.310e-014, alpha -7.473, combined = 5.252e-012 rroots = 5

commencing relation filtering
setting target matrix density to 130.0
estimated available RAM is 16335.2 MB
commencing duplicate removal, pass 1
error -1 reading relation 5647071
read 10M relations
error -1 reading relation 16019318
read 20M relations
read 30M relations
error -15 reading relation 30848927
read 40M relations
read 50M relations
read 60M relations
read 70M relations
read 80M relations
error -1 reading relation 81284589
read 90M relations
read 100M relations
error -9 reading relation 103615619
error -5 reading relation 105019913
read 110M relations
error -9 reading relation 118126460
error -15 reading relation 119657872
read 120M relations
error -15 reading relation 128691353
read 130M relations
error -15 reading relation 136838543
error -9 reading relation 137061557
read 140M relations
read 150M relations
read 160M relations
error -15 reading relation 164230833
read 170M relations
error -1 reading relation 170953599
skipped 7 relations with composite factors
found 18286144 hash collisions in 171198964 relations
added 121573 free relations
commencing duplicate removal, pass 2
found 14191943 duplicates and 157128594 unique relations
memory use: 788.8 MB
reading ideals above 51314688
commencing singleton removal, initial pass
memory use: 3012.0 MB
reading all ideals from disk
memory use: 2730.9 MB
commencing in-memory singleton removal
begin with 157128594 relations and 135251325 unique ideals
reduce to 87672954 relations and 57797685 ideals in 12 passes
max relations containing the same ideal: 30
reading ideals above 720000
commencing singleton removal, initial pass
memory use: 1506.0 MB
reading all ideals from disk
memory use: 3115.8 MB
keeping 63488635 ideals with weight <= 200, target excess is 457059
commencing in-memory singleton removal
begin with 87672955 relations and 63488635 unique ideals
reduce to 87672748 relations and 63488427 ideals in 5 passes
max relations containing the same ideal: 200
removing 8856271 relations and 6856271 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 78816477 relations and 63488427 unique ideals
reduce to 78140759 relations and 55936970 ideals in 7 passes
max relations containing the same ideal: 194
removing 6893882 relations and 4893882 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 71246877 relations and 55936970 unique ideals
reduce to 70786273 relations and 50570297 ideals in 7 passes
max relations containing the same ideal: 183
removing 6352955 relations and 4352955 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 64433318 relations and 50570297 unique ideals
reduce to 64031024 relations and 45804062 ideals in 7 passes
max relations containing the same ideal: 173
removing 6059861 relations and 4059861 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 57971163 relations and 45804062 unique ideals
reduce to 57593357 relations and 41355507 ideals in 7 passes
max relations containing the same ideal: 163
removing 5868402 relations and 3868402 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 51724955 relations and 41355507 unique ideals
reduce to 51353924 relations and 37104229 ideals in 6 passes
max relations containing the same ideal: 148
removing 5733915 relations and 3733915 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 45620009 relations and 37104229 unique ideals
reduce to 45245932 relations and 32983039 ideals in 7 passes
max relations containing the same ideal: 141
removing 5630230 relations and 3630230 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 39615702 relations and 32983039 unique ideals
reduce to 39226630 relations and 28948435 ideals in 6 passes
max relations containing the same ideal: 125
removing 5550898 relations and 3550898 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 33675732 relations and 28948435 unique ideals
reduce to 33257536 relations and 24960972 ideals in 6 passes
max relations containing the same ideal: 113
removing 5487346 relations and 3487346 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 27770190 relations and 24960972 unique ideals
reduce to 27306108 relations and 20985644 ideals in 7 passes
max relations containing the same ideal: 101
removing 5436232 relations and 3436232 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 21869876 relations and 20985644 unique ideals
reduce to 21336478 relations and 16983552 ideals in 7 passes
max relations containing the same ideal: 85
removing 5390287 relations and 3390287 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 15946191 relations and 16983552 unique ideals
reduce to 15299726 relations and 12895906 ideals in 7 passes
max relations containing the same ideal: 65
removing 5021480 relations and 3147849 ideals in 1873631 cliques
commencing in-memory singleton removal
begin with 10278246 relations and 12895906 unique ideals
reduce to 9504951 relations and 8893383 ideals in 8 passes
max relations containing the same ideal: 49
removing 402770 relations and 321391 ideals in 81379 cliques
commencing in-memory singleton removal
begin with 9102181 relations and 8893383 unique ideals
reduce to 9087168 relations and 8556835 ideals in 6 passes
max relations containing the same ideal: 49
relations with 0 large ideals: 1447
relations with 1 large ideals: 13983
relations with 2 large ideals: 168304
relations with 3 large ideals: 806897
relations with 4 large ideals: 1923972
relations with 5 large ideals: 2594214
relations with 6 large ideals: 2124687
relations with 7+ large ideals: 1453664
commencing 2-way merge
reduce to 5914558 relation sets and 5384225 unique ideals
commencing full merge
memory use: 715.4 MB
found 2656321 cycles, need 2622425
weight of 2622425 cycles is about 341310580 (130.15/cycle)
distribution of cycle lengths:
1 relations: 43804
2 relations: 114253
3 relations: 157428
4 relations: 177823
5 relations: 194745
6 relations: 199943
7 relations: 201234
8 relations: 192250
9 relations: 181207
10+ relations: 1159738
heaviest cycle: 28 relations
commencing cycle optimization
start with 25088647 relations
pruned 1350542 relations
memory use: 631.5 MB
distribution of cycle lengths:
1 relations: 43804
2 relations: 117802
3 relations: 165096
4 relations: 187290
5 relations: 207342
6 relations: 212784
7 relations: 215156
8 relations: 204215
9 relations: 192247
10+ relations: 1076689
heaviest cycle: 28 relations
RelProcTime: 4616

commencing linear algebra
read 2622425 cycles
cycles contain 8825315 unique relations
read 8825315 relations
using 20 quadratic characters above 4294917295
building initial matrix
memory use: 1253.3 MB
read 2622425 cycles
matrix is 2622246 x 2622425 (1314.0 MB) with weight 402278277 (153.40/col)
sparse part has weight 312987251 (119.35/col)
filtering completed in 2 passes
matrix is 2622160 x 2622339 (1314.0 MB) with weight 402271878 (153.40/col)
sparse part has weight 312983970 (119.35/col)
matrix starts at (0, 0)
matrix is 2622160 x 2622339 (1314.0 MB) with weight 402271878 (153.40/col)
sparse part has weight 312983970 (119.35/col)
saving the first 48 matrix rows for later
matrix includes 64 packed rows
matrix is 2622112 x 2622339 (1272.9 MB) with weight 345069938 (131.59/col)
sparse part has weight 307458998 (117.25/col)
using block size 8192 and superblock size 589824 for processor cache size 6144 kB
commencing Lanczos iteration (4 threads)
memory use: 1042.8 MB
linear algebra at 0.1%, ETA 3h49m2622339 dimensions (0.1%, ETA 3h49m)
checkpointing every 670000 dimensions339 dimensions (0.1%, ETA 3h57m)
linear algebra completed 2622112 of 2622339 dimensions (100.0%, ETA 0h 0m)
lanczos halted after 41469 iterations (dim = 2622112)
recovered 29 nontrivial dependencies
BLanczosTime: 13908

commencing square root phase
handling dependencies 1 to 64
reading relations for dependency 1
read 1311487 cycles
cycles contain 4413868 unique relations
read 4413868 relations
multiplying 4413868 relations
multiply complete, coefficients have about 247.94 million bits
initial square root is modulo 790382237
sqrtTime: 801
p64 factor: 4444692710947209289525091454575237582953389641202214946375811347
p88 factor: 1103054314249309656255723389110369974683440590926814295761726950367081523893141659321527
elapsed time 05:22:06