[QUOTE=henryzz;548142]ryanp gave in trying to factor 732541^47-1 due to it running into weird issues with lasieve(random low yield on some q if I remember right). I would suggest doing this one purely CADO would be the most sensible way. I think this one would have been done ages ago if it wasn't for this issue.[/QUOTE]

This number was my [URL="https://en.wikipedia.org/wiki/Moby-Dick"]white whale[/URL] for a long time. Indeed, I believe it hit issues with lasieve producing low yield and we judt couldn't get to enough relations to produce a matrix.

Seeing this thread inspired me to re-attempt it with the CADO siever, and lo and behold:

[CODE]Msieve v. 1.54 (SVN 1030M)
GMP: 6.2.0
Sun Jun 21 07:01:29 2020
random seeds: f84b09be a5009ec1
factoring 605716904027877980774625455520189647387776352555063757365644672493136637525085152114527251672682055452329862008130550673203343550128250999766605061023948523297828457779191592093682881010498969046911261346842026672855745883554109771998292748069377018429964450347583969787 (270 digits)
no P-1/P+1/ECM available, skipping
commencing number field sieve (270-digit input)
R0: 82919274927962023982932249248351337261442889121
R1: -1
A0: -732541
A1: 0
A2: 0
A3: 0
A4: 0
A5: 0
A6: 1
skew 1.00, size 1.556e-14, alpha 2.799, combined = 3.971e-15 rroots = 2

commencing linear algebra
read 49504481 cycles
cycles contain 178983010 unique relations
read 178983010 relations
using 20 quadratic characters above 4294917295
building initial matrix
memory use: 23395.4 MB
read 49504481 cycles
matrix is 49504304 x 49504481 (26552.6 MB) with weight 7481507800 (151.13/col)
sparse part has weight 6465550771 (130.61/col)
filtering completed in 2 passes
matrix is 49502913 x 49503083 (26552.5 MB) with weight 7481465351 (151.13/col)
sparse part has weight 6465536967 (130.61/col)
matrix starts at (0, 0)
matrix is 49502913 x 49503083 (26552.5 MB) with weight 7481465351 (151.13/col)
sparse part has weight 6465536967 (130.61/col)
saving the first 240 matrix rows for later
matrix includes 256 packed rows
matrix is 49502673 x 49503083 (24863.2 MB) with weight 5972250562 (120.64/col)
sparse part has weight 5725692792 (115.66/col)
using block size 8192 and superblock size 608256 for processor cache size 25344 kB
commencing Lanczos iteration (36 threads)
memory use: 33219.3 MB
linear algebra at 0.0%, ETA 548h56m503083 dimensions (0.0%, ETA 548h56m)
checkpointing every 90000 dimensions03083 dimensions (0.0%, ETA 552h42m)
linear algebra completed 32678 of 49503083 dimensions (0.1%, ETA 555h 5m)[/CODE]

732541^47-1
 

Update: with some more relations and a faster machine, managed to squeeze the LA time for (732541^47-1)/732540 down to ~250hrs.

Ryan-
What settings & parameters did you use? How many relations did you collect (for the first matrix, or also the final number)?

[QUOTE=VBCurtis;548942]Ryan-
What settings & parameters did you use? How many relations did you collect (for the first matrix, or also the final number)?[/QUOTE]

CADO "las" siever; -I 16, lpbr=lpba=33. I collected about 900M unique relations for the final matrix, which ended up being 42M rows/cols.

[CODE]Msieve v. 1.54 (SVN 1030M)
Tue Jun 23 14:53:19 2020
random seeds: 985e1878 b653abc6
factoring 605716904027877980774625455520189647387776352555063757365644672493136637525085152114527251672682055452329862008130550673203343550128250999766605061023948523297828457779191592093682881010498969046911261346842026672855745883554109771998292748069377018429964450347583969787 (270 digits)
no P-1/P+1/ECM available, skipping
commencing number field sieve (270-digit input)
R0: 82919274927962023982932249248351337261442889121
R1: -1
A0: -732541
A1: 0
A2: 0
A3: 0
A4: 0
A5: 0
A6: 1
skew 1.00, size 1.556e-14, alpha 2.799, combined = 3.971e-15 rroots = 2

commencing linear algebra
matrix starts at (0, 0)
matrix is 42025294 x 42025465 (23805.1 MB) with weight 6697281955 (159.36/col)
sparse part has weight 5820099165 (138.49/col)
saving the first 240 matrix rows for later
matrix includes 256 packed rows
matrix is 42025054 x 42025465 (22221.9 MB) with weight 5375881265 (127.92/col)
sparse part has weight 5152937798 (122.61/col)
using block size 8192 and superblock size 946176 for processor cache size 39424 kB
commencing Lanczos iteration (64 threads)
memory use: 29170.0 MB
restarting at iteration 5705 (dim = 1456120)
linear algebra at 3.5%, ETA 323h26m 42025465 dimensions (3.5%, ETA 323h26m)
checkpointing every 130000 dimensions2025465 dimensions (3.5%, ETA 325h16m)
linear algebra completed 2353062 of 42025465 dimensions (5.6%, ETA 254h50m) [/CODE]

It is great news that this one will soon now be put to bed. This number has bugged me since you struggled with it originally. :smile:

732541^47-1
 

LA for 732541^47-1 has completed:

[CODE]linear algebra completed 42024960 of 42025465 dimensions (100.0%, ETA 0h 0m)
lanczos halted after 164654 iterations (dim = 42025052)
recovered 35 nontrivial dependencies
BLanczosTime: 887925[/CODE]

Starting square root phase now.

732541^47-1
 

At long last... the beast is slain!

[CODE]Fri Jul 3 21:38:12 2020 Msieve v. 1.54 (SVN 1030M)
Fri Jul 3 21:38:12 2020 random seeds: 177225fc d79499b7
Fri Jul 3 21:38:12 2020 factoring 605716904027877980774625455520189647387776352555063757365644672493136637525085152114527251672682055452329862008130550673203343550128250999766605061023948523297828457779191592093682881010498969046911261346842026672855745883554109771998292748069377018429964450347583969787 (270 digits)
Fri Jul 3 21:38:13 2020 no P-1/P+1/ECM available, skipping
Fri Jul 3 21:38:13 2020 commencing number field sieve (270-digit input)
Fri Jul 3 21:38:13 2020 R0: 82919274927962023982932249248351337261442889121
Fri Jul 3 21:38:13 2020 R1: -1
Fri Jul 3 21:38:13 2020 A0: -732541
Fri Jul 3 21:38:13 2020 A1: 0
Fri Jul 3 21:38:13 2020 A2: 0
Fri Jul 3 21:38:13 2020 A3: 0
Fri Jul 3 21:38:13 2020 A4: 0
Fri Jul 3 21:38:13 2020 A5: 0
Fri Jul 3 21:38:13 2020 A6: 1
Fri Jul 3 21:38:13 2020 skew 1.00, size 1.556e-14, alpha 2.799, combined = 3.971e-15 rroots = 2
Fri Jul 3 21:38:13 2020
Fri Jul 3 21:38:13 2020 commencing square root phase
...
Sat Jul 4 05:09:14 2020 reading relations for dependency 3
Sat Jul 4 05:09:21 2020 read 21008674 cycles
Sat Jul 4 05:11:17 2020 cycles contain 76741288 unique relations
Sat Jul 4 05:36:26 2020 read 76741288 relations
Sat Jul 4 05:50:29 2020 multiplying 76741288 relations
Sat Jul 4 07:19:29 2020 multiply complete, coefficients have about 2281.91 million bits
Sat Jul 4 07:19:39 2020 initial square root is modulo 131251
Sat Jul 4 08:54:10 2020 sqrtTime: 40557
Sat Jul 4 08:54:10 2020 p97 factor: 2819547582804944662558506166260442570490634075065671086863661333487318228728167329126982576206037
Sat Jul 4 08:54:10 2020 p174 factor: 214827693535605520238170356773073656092324091170876661367255562401621577099854750475504080344557764599470617993196489447188419494653562837204127188167240517147306600526628751
Sat Jul 4 08:54:10 2020 elapsed time 11:15:58[/CODE]

Pascal is going to get excited over this one.

Oh wait, it is already removed from the MWRB file!

[QUOTE=ryanp;549735]At long last... the beast is slain!
[/QUOTE]
Yay CADO! Yay Ryan!!

[QUOTE=RichD;549743]Pascal is going to get excited over this one.

Oh wait, it is already removed from the MWRB file![/QUOTE]

I noticed that as well. Does that file auto-update from factordb?

Yes, it is good to see this one down. Thank you very much, Ryan!
No auto-update, I removed the line from the MWRB file.
The weight of the remaining composites will be updated in a month or so.
732541 is (29^5-1)/28, so (732541^47-1)/732540 was also a composite of interest for lower bounds on the total number of prime factors.