Now what (IV)

[akruppa]

A large part of the reason why I started focussing on the base 3 tables some... hmm, how long's it been... six or seven years ago?... was that the largest remaining composite for 3- and 3+ was smaller than for the other Cunningham bases, so I figured those would have the best chance of clearing them out completely. Plus, it's an odd prime, so some of those factorisations might perhaps help someone who needs the structure of some GF(3^n)*, or maybe advance OPN search a little bit.

Alex

[bdodson]

Originally Posted by akruppa

A large part of the reason why I started focussing on the base 3 tables some... hmm, how long's it been... six or seven years ago?... was that the largest remaining composite for 3- and 3+ was smaller than for the other Cunningham bases, so I figured those would have the best chance of clearing them out completely. Plus, it's an odd prime, so some of those factorisations might perhaps help someone who needs the structure of some GF(3^n)*, or maybe advance OPN search a little bit.

Alex

The Garo/Rogue tables for 5+ and 7+ still take most of two full pages,
but 11- and 11+ are both short. For 3- we'll need snfs 280, twice?
Looks like two more in 3+. The lists for 5- and 7- also fit on a single
page. Not sure what would trigger an extension; perhaps Paul or Bob
know? One notable feature, aside from completely clearing both + and
- might be a number of bases + or - with fewer than five "first holes".
We're not that far from putting some blank spots on that part of the
"champions" page at Sam's site. -Bruce

PS - perhaps someone could find snfs difficulties on some of the
other short tables, like on Alex's 3-?

[bdodson]

Originally Posted by bdodson

...
PS - perhaps someone could find snfs difficulties on some of the
other short tables, like on Alex's 3-?

That was quick (3+ and 11-+). There are several other short (one page
in the Cunningham subforum) lists. Both 12- and 12+ are short. The
others are minus only, base-6 and base-10. Perhaps it's worth emphasizing
that this is not a topic for which participation is limited to those with
either access to large University machines or top-of-the-line icore-7s.
The new Selfridge + Wagstaff wanted lists include a bunch of 3+ numbers
(in particular), and typically focus on neglected numbers that are easier
relative to numbers that take more extensive resources. Sustained
persistence being the primary resource.

I've no idea what Cunningham et. al. (back in the 1920's?) were thinking,
but perhaps the base-b lists with b composite serve as test cases for seeing
whether there's a visible difference, aside from ones already known, with
the factorization tables for the prime bases. Base-10 has its own interest
(and long focus of attention) from repunit (1111...111's) factorizations.
Base-12 is most likely short due to sustained attention from Peter/CWI.
Among all bases there's a special interest in numbers with few/small
non-algebraic factors (number of digits close to snfs difficulty), and
especially b^q-1, b^q+1 for prime exponents, M_p's for example.

Thanks are due to Alex and (most recently) Batalov for attention to updating
the forum tables. -Bruce

[bdodson]

Originally Posted by bdodson

... A number that has been ecm'd is

c238 3^551 - 1 (SNFS  262.89)

although Batalov has already looked at parameters (and might reserve
it soon for Batalov+Dodson? ... we could find another one). ... -bd

We took 10, 393+ (and one each from 11- and 12+) as warm-up for
2, 2086M, so 3,551- is no longer on the list of numbers we might consider
reserving any time soon --- i.e., open; un-encumbered for the forum.
Being from c234-c250 it had 2t50 to start. The second (last?) round of
ecm finished over the weekend, 10325 curves with B1 = 260M (p60-optimal;
default B2) a new 6.5*t50; should be ready to sieve if you like. -Bruce

[bdodson]

Originally Posted by bdodson

...The second (last?) round of
ecm finished over the weekend, 10325 curves with B1 = 260M (p60-optimal;
default B2) a new 6.5*t50; should be ready to sieve if you like. -Bruce

OK, nevermind the curve counts on 3, 551-. For M859 C203 diff 258.58
it's below c233, which is good; then above diff 250 means 3t50, just
counting Lehigh curves. Must have had a bunch more from other people
as a Mersenne number. -bd

[Batalov]

The convenience detour is here
=> http://www.mersenneforum.org/showthread.php?t=11761