Now what (IV)
 

109!+1 is proceeding nicely.

10^263-1 may or may not finish its linear algebra before I leave the country, but it'll certainly be done by Easter.

What would you be interested in next? I don't see any very interesting but possible GNFS numbers from the Cunningham tables - most of the C180 to C185 are easier by SNFS. Siever 16e isn't yet really usable, which makes very hard SNFS jobs a bit out of reach.

Possibilities are:

2^877-1 (Mersenne, SNFS, a bit harder than 10^263-1)

2801^79-1 (oddperfect, SNFS, a bit harder than 2^877-1)

EM43 (GNFS, people on this forum have been attacking it on and off for several years, same sort of difficulty as 5^421-1 was)

Something else

[QUOTE=fivemack;167269]109!+1 is proceeding nicely.

10^263-1 may or may not finish its linear algebra before I leave the country, but it'll certainly be done by Easter.

What would you be interested in next? I don't see any very interesting but possible GNFS numbers from the Cunningham tables - most of the C180 to C185 are easier by SNFS. Siever 16e isn't yet really usable, which makes very hard SNFS jobs a bit out of reach.

Possibilities are:

2^877-1 (Mersenne, SNFS, a bit harder than 10^263-1)

2801^79-1 (oddperfect, SNFS, a bit harder than 2^877-1)

EM43 (GNFS, people on this forum have been attacking it on and off for several years, same sort of difficulty as 5^421-1 was)

Something else[/QUOTE]

I'd vote for EM43 and would probably dedicate resources to it were it to be done. The interesting thing about this value is that nothing further work can be done on the sequence until EM43 is factored. The others can't be considered "roadblocks" for their respective projects as there are other Mersenne or Odd-Perfect numbers available to factor.

[QUOTE=fivemack;167269]109!+1 is proceeding nicely.

10^263-1 may or may not finish its linear algebra before I leave the country, but it'll certainly be done by Easter.

What would you be interested in next? I don't see any very interesting but possible GNFS numbers from the Cunningham tables - most of the C180 to C185 are easier by SNFS. Siever 16e isn't yet really usable, which makes very hard SNFS jobs a bit out of reach.

Possibilities are:

2^877-1 (Mersenne, SNFS, a bit harder than 10^263-1)

2801^79-1 (oddperfect, SNFS, a bit harder than 2^877-1)

EM43 (GNFS, people on this forum have been attacking it on and off for several years, same sort of difficulty as 5^421-1 was)

Something else[/QUOTE]

11,233+ or 11,229-.

The factorization of 10[sup]271[/sup]-1 could help to find more prime [URL="http://www.alpertron.com.ar/googolm.pl"]factors of googolplex-10[/URL].

[quote=fivemack;167269]109!+1 is proceeding nicely.

10^263-1 may or may not finish its linear algebra before I leave the country, but it'll certainly be done by Easter.

What would you be interested in next? I don't see any very interesting but possible GNFS numbers from the Cunningham tables - most of the C180 to C185 are easier by SNFS. Siever 16e isn't yet really usable, which makes very hard SNFS jobs a bit out of reach.

Possibilities are:

2^877-1 (Mersenne, SNFS, a bit harder than 10^263-1)

2801^79-1 (oddperfect, SNFS, a bit harder than 2^877-1)

EM43 (GNFS, people on this forum have been attacking it on and off for several years, same sort of difficulty as 5^421-1 was)

Something else[/quote]

I'd go for 2^877-1 first on the grounds that this is the mersenneforum, and then EM43. This both avoids two GNFSs in a row and allows more time for improvements in msieve's poly selection.

[QUOTE=R.D. Silverman;167276]11,233+ or 11,229-.[/QUOTE]

Heck, I'll do those two. Should be about 30 days and 25 days of sieving, respectively, on my currently-available resources. I'm surprised they are still uncracked.

I'll send off a missive to Wagstaff, and grab one of these.

I finished 11,227- a while ago. I thought that 11,229- was already reserved, but a glance at the Cunningham project page says it hasn't.

[tex]\ 2^{877}-1[/tex]

I'd also like to see M877 factored.
(Not sure if I'm able again to contribute...)

That looks a reasonable consensus for 2-877. When I get back after Easter, I'll put up a reservations post; until then, please sieve 109!+1 more, so that the matrix doesn't take eight weeks.

[QUOTE=fivemack;167540]That looks a reasonable consensus for 2-877. When I get back after Easter, I'll put up a reservations post; until then, please sieve 109!+1 more, so that the matrix doesn't take eight weeks.[/QUOTE]

This one is C178 with difficulty 264. As a number below C190, it ought
to have had 7*t50 >> t55 worth of ecm ("smallest 100 Cunninghams" list).
I could add another t55 (to make p54/p55's less likely, while not ruling
out p59/p60's), if that would be regarded as a worthwhile contribution?
-Bruce

Another t55 would definitely be a worthwhile contribution, thanks very much for the offer.