65554_220

Msieve v. 1.53 (SVN 1005)
Mon Jul 17 15:58:06 2023
random seeds: e7b058ac 93280fe0
factoring 1563661861115668622918190097163523960929552903790464635843498672861538737025643807076100980868608234301559308211057067594683462516777722769917609 (145 digits)
searching for 15-digit factors
commencing number field sieve (145-digit input)
R0: -9504174850506882983743140603
R1: 1072054602504492318967
A0: 559568459541985326118331278270560
A1: 1470341240286241229557762636
A2: -99555845032205526459195
A3: -313514358865345297
A4: 1463663737536
A5: -1854720
skew 218279.55, size 4.910e-014, alpha -6.877, combined = 1.136e-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 -5 reading relation 5088021
read 10M relations
error -15 reading relation 19981426
read 20M relations
error -9 reading relation 28513824
read 30M relations
error -9 reading relation 36169605
read 40M relations
error -9 reading relation 40059928
error -15 reading relation 40506153
read 50M relations
skipped 8 relations with composite factors
found 7359084 hash collisions in 54113129 relations
added 121693 free relations
commencing duplicate removal, pass 2
found 6079293 duplicates and 48155529 unique relations
memory use: 213.2 MB
reading ideals above 720000
commencing singleton removal, initial pass
memory use: 1378.0 MB
reading all ideals from disk
memory use: 1648.6 MB
keeping 42284892 ideals with weight <= 200, target excess is 263801
commencing in-memory singleton removal
begin with 48155529 relations and 42284892 unique ideals
reduce to 30381209 relations and 22809040 ideals in 12 passes
max relations containing the same ideal: 156
removing 3875402 relations and 2875402 ideals in 1000000 cliques
commencing in-memory singleton removal
begin with 26505807 relations and 22809040 unique ideals
reduce to 26134020 relations and 19546984 ideals in 8 passes
max relations containing the same ideal: 139
removing 3130452 relations and 2130452 ideals in 1000000 cliques
commencing in-memory singleton removal
begin with 23003568 relations and 19546984 unique ideals
reduce to 22739772 relations and 17143036 ideals in 6 passes
max relations containing the same ideal: 126
removing 2932979 relations and 1932979 ideals in 1000000 cliques
commencing in-memory singleton removal
begin with 19806793 relations and 17143036 unique ideals
reduce to 19562652 relations and 14956221 ideals in 7 passes
max relations containing the same ideal: 113
removing 2836785 relations and 1836785 ideals in 1000000 cliques
commencing in-memory singleton removal
begin with 16725867 relations and 14956221 unique ideals
reduce to 16478210 relations and 12860785 ideals in 7 passes
max relations containing the same ideal: 101
removing 2782236 relations and 1782236 ideals in 1000000 cliques
commencing in-memory singleton removal
begin with 13695974 relations and 12860785 unique ideals
reduce to 13428265 relations and 10797071 ideals in 7 passes
max relations containing the same ideal: 87
removing 2748895 relations and 1748895 ideals in 1000000 cliques
commencing in-memory singleton removal
begin with 10679370 relations and 10797071 unique ideals
reduce to 10372761 relations and 8722448 ideals in 8 passes
max relations containing the same ideal: 77
removing 2725464 relations and 1725464 ideals in 1000000 cliques
commencing in-memory singleton removal
begin with 7647297 relations and 8722448 unique ideals
reduce to 7268720 relations and 6587461 ideals in 8 passes
max relations containing the same ideal: 57
removing 1203591 relations and 828342 ideals in 375249 cliques
commencing in-memory singleton removal
begin with 6065129 relations and 6587461 unique ideals
reduce to 5927259 relations and 5614584 ideals in 7 passes
max relations containing the same ideal: 53
relations with 0 large ideals: 871
relations with 1 large ideals: 5466
relations with 2 large ideals: 71506
relations with 3 large ideals: 383739
relations with 4 large ideals: 1050104
relations with 5 large ideals: 1628723
relations with 6 large ideals: 1531378
relations with 7+ large ideals: 1255472
commencing 2-way merge
reduce to 3871600 relation sets and 3558925 unique ideals
commencing full merge
memory use: 477.0 MB
found 1822789 cycles, need 1783125
weight of 1783125 cycles is about 196376474 (110.13/cycle)
distribution of cycle lengths:
1 relations: 45649
2 relations: 97963
3 relations: 127834
4 relations: 140498
5 relations: 151855
6 relations: 152934
7 relations: 149613
8 relations: 142172
9 relations: 131262
10+ relations: 643345
heaviest cycle: 24 relations
commencing cycle optimization
start with 14845200 relations
pruned 719809 relations
memory use: 396.7 MB
distribution of cycle lengths:
1 relations: 45649
2 relations: 100864
3 relations: 134186
4 relations: 147458
5 relations: 161369
6 relations: 161972
7 relations: 159234
8 relations: 150204
9 relations: 137802
10+ relations: 584387
heaviest cycle: 24 relations
RelProcTime: 1235

commencing linear algebra
read 1783125 cycles
cycles contain 5747002 unique relations
read 5747002 relations
using 20 quadratic characters above 4294917295
building initial matrix
memory use: 789.8 MB
read 1783125 cycles
matrix is 1782946 x 1783125 (768.9 MB) with weight 238465013 (133.73/col)
sparse part has weight 181961025 (102.05/col)
filtering completed in 2 passes
matrix is 1782828 x 1783007 (768.9 MB) with weight 238456137 (133.74/col)
sparse part has weight 181956220 (102.05/col)
matrix starts at (0, 0)
matrix is 1782828 x 1783007 (768.9 MB) with weight 238456137 (133.74/col)
sparse part has weight 181956220 (102.05/col)
saving the first 48 matrix rows for later
matrix includes 64 packed rows
matrix is 1782780 x 1783007 (748.0 MB) with weight 201245601 (112.87/col)
sparse part has weight 178265263 (99.98/col)
using block size 8192 and superblock size 589824 for processor cache size 6144 kB
commencing Lanczos iteration (4 threads)
memory use: 609.1 MB
linear algebra at 0.1%, ETA 1h57m1783007 dimensions (0.1%, ETA 1h57m)
checkpointing every 910000 dimensions007 dimensions (0.1%, ETA 1h57m)
linear algebra completed 1782621 of 1783007 dimensions (100.0%, ETA 0h 0m)
lanczos halted after 28192 iterations (dim = 1782780)
recovered 33 nontrivial dependencies
BLanczosTime: 5500

commencing square root phase
handling dependencies 1 to 64
reading relations for dependency 1
read 891135 cycles
cycles contain 2871972 unique relations
read 2871972 relations
multiplying 2871972 relations
multiply complete, coefficients have about 155.76 million bits
initial square root is modulo 389047
GCD is 1, no factor found
reading relations for dependency 2
read 890492 cycles
cycles contain 2870964 unique relations
read 2870964 relations
multiplying 2870964 relations
multiply complete, coefficients have about 155.71 million bits
initial square root is modulo 387403
GCD is N, no factor found
reading relations for dependency 3
read 890914 cycles
cycles contain 2872490 unique relations
read 2872490 relations
multiplying 2872490 relations
multiply complete, coefficients have about 155.78 million bits
initial square root is modulo 389783
sqrtTime: 1530
p49 factor: 7672105683329452214475082154739385922817711955121
p96 factor: 203811303657262529603406604468785905800498597069108054606007804524371665225390891794887222667129