The factorization of primorials +/- 1

[Joppe_Bos]

rogue: When I have some more spare time I will look into the process of setting up an ECMNet Server, if this will result in more contributions than it is definitely worth the time. Thanks for the tip!

jasong: No problem! If your only real trouble is compiling ecm than it shouldn't be that difficult. PM me if you run Linux and I can probably help you out, unfortunately I know nothing about Windows.

[sean]

Originally Posted by jasong

I'm reserving 76#+1 here (Edit: and 82#+1), since I figure this is the most obvious place. If someone wants to give me editing privileges, I'll restrict myself to this thread and only handle the tracking.(I would suck as a mod, but I'm sure people already know that)

I already ran 4590 curves with B1=11e6 on P76#+1 and 1870 curves B1=11e6 on P84#-1.

Also, note the notation 76#+1 as used at WIFC is nonstandard. I believe it is more usual to write p#+1 where p is the largest prime in the product. For this reason I tend to add a "P" to the front when using the WIFC style of notation.

[Joppe_Bos]

Originally Posted by sean

I already ran 4590 curves with B1=11e6 on P76#+1 and 1870 curves B1=11e6 on P84#-1.

Also, note the notation 76#+1 as used at WIFC is nonstandard. I believe it is more usual to write p#+1 where p is the largest prime in the product. For this reason I tend to add a "P" to the front when using the WIFC style of notation.

Thanks for helping out Sean, I will incorporate your ECM curves in my tables here.

I ran the following curves:

5688 curves with B1=11e6 on P84# - 1
4084 curves with B1=11e6 on P86# - 1
2790 curves with B1=11e6 on P89# - 1

2500 curves with B1=3e6 on P103# - 1
2500 curves with B1=3e6 on P104# - 1
2500 curves with B1=3e6 on P114# - 1
2500 curves with B1=3e6 on P118# - 1
2500 curves with B1=3e6 on P119# - 1

After checking all the remaining composites I found two errors:
the c269 of P133# + 1 and c298 of P134# + 1 turned out to be prime. So two less composites for the primorials + 1 table!

[fivemack]

May I reserve 109#+1 (the C143); it ought to take a couple of weeks by GNFS on four cores. I'll also run 110#+1 with ECM 11M on another dual-core for a week or so, which ought to get to t45.

[Joppe_Bos]

Originally Posted by fivemack

May I reserve 109#+1 (the C143); it ought to take a couple of weeks by GNFS on four cores. I'll also run 110#+1 with ECM 11M on another dual-core for a week or so, which ought to get to t45.

Great! I updated the tables to indicate you run GNFS on this number. I will mainly concentrate on the larger P# - 1 numbers to finish all the remaining 2500 curves with B1=3e6.

[fivemack]

5000 curves at B1=11M on P110 (~140 hours, idle time of a dual-core system); no factor found

[Joppe_Bos]

Originally Posted by fivemack

5000 curves at B1=11M on P110 (~140 hours, idle time of a dual-core system); no factor found

Great! I updated the tables and also incorperated my new curves and factors.

I found four more factors including two for P157# - 1 which finishes this number.

P139# - 1 (c315) = p36 * c279
With p36 = 340880743122446342921525125913540909

P141# - 1 (c293) = p41 * c253
With p41 = 10156928967008289071331709863959789982611

P157# - 1 : c380 = p36 * p40 * p305
With p36 = 997030379084688575361184144236643271
and p40 = 1677036798638480081836623887018471486963

Done 1020 curves on P96# - 1 with B1=11e6
Done 1020 curves on P103# - 1 with B1=11e6

Done 2900 curves on P120# - 1 with B1=3e6
Done 2900 curves on P121# - 1 with B1=3e6
Done 2900 curves on P122# - 1 with B1=3e6
Done 2900 curves on P123# - 1 with B1=3e6
Done 2900 curves on P139# - 1 with B1=3e6
Done 2900 curves on P140# - 1 with B1=3e6
Done 2900 curves on P141# - 1 with B1=3e6

[fivemack]

Running 2400 curves @ 3e6 on P160+, should take ~36 hours, then will proceed to P159+ and so on.

For the P109+ 143-digit GNFS, I've found a decent polynomial and good sieving parameters, I find about seven relations per second per CPU and need forty million. I'll leave two CPUs running while I'm on vacation in mid-September, but probably won't have factors until the start of October - I'm doing two quite large GNFS jobs at once, have only four CPUs to use, and think it would be unkind to spend my lodger's rent checks on quad-core boxes.

[fivemack]

2400 @ 3e6 on P160+; no factor

[Joppe_Bos]

Done 2520 curves on P111# - 1 with B1=3e6
Done 2900 curves on P112# - 1 with B1=3e6
Done 2500 curves on P126# - 1 with B1=3e6

Found a 38-digit factor which finishes the factorization of P142# - 1
P142# - 1 (c295) = p38 * p258
With p38 = 18303018932796265837451137127995991537

And a new one for P154# - 1:
P154# - 1 (c370) = p32 * c339
With p32 = 10863458068568643283688118471511

Tables have been updated.

[rogue]

Have you done any P-1 or P+1 factoring on these numbers?