32224_211

Msieve v. 1.53 (SVN 1005)
Tue Jul 18 14:07:54 2023
random seeds: 8ce2b0c4 d70fd24f
factoring 2045617183379621340739851731682683476058770311491715932906355206610919291197178161669143133925518394853595837934593769322658266511700847582090023 (145 digits)
searching for 15-digit factors
commencing number field sieve (145-digit input)
R0: -6553867227187827772076939287
R1: 133768967348066089787
A0: 18457895325690492123403135508184
A1: -693864896740981682002085229
A2: -76049339974208991038206
A3: 294532598827924811
A4: 5564610874980
A5: 10036800
skew 118375.46, size 5.184e-014, alpha -6.635, combined = 1.168e-011 rroots = 5

commencing relation filtering
setting target matrix density to 110.0
estimated available RAM is 16335.2 MB
commencing duplicate removal, pass 1
read 10M relations
error -5 reading relation 10565990
error -15 reading relation 10571410
error -5 reading relation 10605264
error -1 reading relation 13997050
error -9 reading relation 16809959
read 20M relations
read 30M relations
read 40M relations
read 50M relations
error -9 reading relation 57652475
error -15 reading relation 58128782
error -9 reading relation 58372064
read 60M relations
read 70M relations
error -9 reading relation 73421788
read 80M relations
error -1 reading relation 88181454
read 90M relations
read 100M relations
error -9 reading relation 108892911
error -15 reading relation 108896578
error -1 reading relation 109631175
read 110M relations
skipped 6 relations with composite factors
found 8829172 hash collisions in 110440132 relations
added 122055 free relations
commencing duplicate removal, pass 2
found 4363132 duplicates and 106199055 unique relations
memory use: 394.4 MB
reading ideals above 59965440
commencing singleton removal, initial pass
memory use: 1506.0 MB
reading all ideals from disk
memory use: 1739.8 MB
commencing in-memory singleton removal
begin with 106199055 relations and 77964489 unique ideals
reduce to 74389390 relations and 43679030 ideals in 10 passes
max relations containing the same ideal: 148
reading ideals above 720000
commencing singleton removal, initial pass
memory use: 1378.0 MB
reading all ideals from disk
memory use: 2642.3 MB
keeping 50434318 ideals with weight <= 200, target excess is 363976
commencing in-memory singleton removal
begin with 74389390 relations and 50434318 unique ideals
reduce to 74388923 relations and 50433851 ideals in 5 passes
max relations containing the same ideal: 200
removing 6876600 relations and 4876600 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 67512323 relations and 50433851 unique ideals
reduce to 67019620 relations and 45048274 ideals in 7 passes
max relations containing the same ideal: 197
removing 5674643 relations and 3674643 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 61344977 relations and 45048274 unique ideals
reduce to 61014051 relations and 41032903 ideals in 6 passes
max relations containing the same ideal: 185
removing 5354957 relations and 3354957 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 55659094 relations and 41032903 unique ideals
reduce to 55373104 relations and 37383347 ideals in 6 passes
max relations containing the same ideal: 175
removing 5180984 relations and 3180984 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 50192120 relations and 37383347 unique ideals
reduce to 49925145 relations and 33927029 ideals in 6 passes
max relations containing the same ideal: 163
removing 5060318 relations and 3060318 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 44864827 relations and 33927029 unique ideals
reduce to 44602687 relations and 30595525 ideals in 6 passes
max relations containing the same ideal: 152
removing 4974191 relations and 2974191 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 39628496 relations and 30595525 unique ideals
reduce to 39361728 relations and 27344697 ideals in 6 passes
max relations containing the same ideal: 142
removing 4911203 relations and 2911203 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 34450525 relations and 27344697 unique ideals
reduce to 34171675 relations and 24143146 ideals in 6 passes
max relations containing the same ideal: 127
removing 4855741 relations and 2855741 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 29315934 relations and 24143146 unique ideals
reduce to 29014223 relations and 20972165 ideals in 6 passes
max relations containing the same ideal: 115
removing 4815103 relations and 2815103 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 24199120 relations and 20972165 unique ideals
reduce to 23861204 relations and 17801499 ideals in 6 passes
max relations containing the same ideal: 98
removing 4781129 relations and 2781129 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 19080075 relations and 17801499 unique ideals
reduce to 18682081 relations and 14597421 ideals in 7 passes
max relations containing the same ideal: 85
removing 4753215 relations and 2753215 ideals in 2000000 cliques
commencing in-memory singleton removal
begin with 13928866 relations and 14597421 unique ideals
reduce to 13423710 relations and 11299606 ideals in 8 passes
max relations containing the same ideal: 68
removing 4094422 relations and 2392531 ideals in 1701891 cliques
commencing in-memory singleton removal
begin with 9329288 relations and 11299606 unique ideals
reduce to 8704053 relations and 8221643 ideals in 8 passes
max relations containing the same ideal: 52
removing 301942 relations and 241745 ideals in 60197 cliques
commencing in-memory singleton removal
begin with 8402111 relations and 8221643 unique ideals
reduce to 8389487 relations and 7967152 ideals in 6 passes
max relations containing the same ideal: 49
relations with 0 large ideals: 1193
relations with 1 large ideals: 8294
relations with 2 large ideals: 108554
relations with 3 large ideals: 557765
relations with 4 large ideals: 1472172
relations with 5 large ideals: 2244862
relations with 6 large ideals: 2137735
relations with 7+ large ideals: 1858912
commencing 2-way merge
reduce to 5996498 relation sets and 5574163 unique ideals
commencing full merge
memory use: 682.7 MB
found 2665181 cycles, need 2636363
weight of 2636363 cycles is about 290434901 (110.16/cycle)
distribution of cycle lengths:
1 relations: 97733
2 relations: 166379
3 relations: 215033
4 relations: 231697
5 relations: 237606
6 relations: 227822
7 relations: 210296
8 relations: 187447
9 relations: 165373
10+ relations: 896977
heaviest cycle: 28 relations
commencing cycle optimization
start with 21863519 relations
pruned 1276070 relations
memory use: 568.6 MB
distribution of cycle lengths:
1 relations: 97733
2 relations: 172164
3 relations: 227218
4 relations: 245612
5 relations: 253976
6 relations: 242564
7 relations: 223091
8 relations: 196585
9 relations: 171563
10+ relations: 805857
heaviest cycle: 28 relations
RelProcTime: 3073

commencing linear algebra
read 2636363 cycles
cycles contain 8178038 unique relations
read 8178038 relations
using 20 quadratic characters above 4294917295
building initial matrix
memory use: 1135.3 MB
read 2636363 cycles
matrix is 2636183 x 2636363 (1123.7 MB) with weight 343934140 (130.46/col)
sparse part has weight 265577524 (100.74/col)
filtering completed in 2 passes
matrix is 2635844 x 2636023 (1123.7 MB) with weight 343916103 (130.47/col)
sparse part has weight 265570625 (100.75/col)
matrix starts at (0, 0)
matrix is 2635844 x 2636023 (1123.7 MB) with weight 343916103 (130.47/col)
sparse part has weight 265570625 (100.75/col)
saving the first 48 matrix rows for later
matrix includes 64 packed rows
matrix is 2635796 x 2636023 (1093.6 MB) with weight 290325489 (110.14/col)
sparse part has weight 260321331 (98.76/col)
using block size 8192 and superblock size 589824 for processor cache size 6144 kB
commencing Lanczos iteration (4 threads)
memory use: 893.4 MB
linear algebra at 0.1%, ETA 2h53m2636023 dimensions (0.1%, ETA 2h53m)
checkpointing every 820000 dimensions023 dimensions (0.1%, ETA 3h14m)
linear algebra completed 2635660 of 2636023 dimensions (100.0%, ETA 0h 0m)
lanczos halted after 41684 iterations (dim = 2635792)
recovered 27 nontrivial dependencies
BLanczosTime: 14498

commencing square root phase
handling dependencies 1 to 64
reading relations for dependency 1
read 1319221 cycles
cycles contain 4091538 unique relations
read 4091538 relations
multiplying 4091538 relations
multiply complete, coefficients have about 234.01 million bits
initial square root is modulo 250059079
GCD is 1, no factor found
reading relations for dependency 2
read 1319012 cycles
cycles contain 4093068 unique relations
read 4093068 relations
multiplying 4093068 relations
multiply complete, coefficients have about 234.10 million bits
initial square root is modulo 251865553
GCD is 1, no factor found
reading relations for dependency 3
read 1317854 cycles
cycles contain 4088312 unique relations
read 4088312 relations
multiplying 4088312 relations
multiply complete, coefficients have about 233.83 million bits
initial square root is modulo 246260107
GCD is N, no factor found
reading relations for dependency 4
read 1317590 cycles
cycles contain 4088534 unique relations
read 4088534 relations
multiplying 4088534 relations
multiply complete, coefficients have about 233.84 million bits
initial square root is modulo 246538543
GCD is N, no factor found
reading relations for dependency 5
read 1318370 cycles
cycles contain 4089326 unique relations
read 4089326 relations
multiplying 4089326 relations
multiply complete, coefficients have about 233.88 million bits
initial square root is modulo 247337869
sqrtTime: 3446
p71 factor: 25480866580926583249254478083097092662714984125733456685559946365649179
p74 factor: 80280518595503542602348789893666362740797600481321545920508505721650897637
elapsed time 05:50:18