[QUOTE=R.D. Silverman;234414]However, I am curious as to why time was spent on this number. What made it important? Have the Brent tables been extended to all bases less than 1000? What is special about base = 971?[/QUOTE]

Richard Brent has for many years published two tables of factorizations. These were both available from his Oxford page, and are now available from his Australian National University page at [url]http://wwwmaths.anu.edu.au/~brent/factors.html[/url].

The smaller table is usually called the "Extended Cunningham Table" and covers bases 13-99. The larger table has always covered bases 2 to 9999 and exponents 2 to 9999. This is the table I refer to as "Brent's".

Pace Nielsen has some theorems that apply when p^n-1 has at least two factors larger than 10^11. He prefers to show such factors because that is easier for people to verify, and would like to show those factors for prime bases less than 1000 and p^n < 10^300. Some of these numbers fall in the range suitable for RSALS, and we have been systematically factoring those numbers. We originally fed numbers from SNFS 220 to 250 - this was the last of these numbers that had no known factors of any size.

William

[QUOTE=debrouxl;234417]...Maybe 2t50 for all tasks of SNFS difficulty above, say, 238, could be manageable, however ?[/QUOTE]
Yes, that's what I meant. ...then 3t50, 4t50 etc. on a sliding scale.

Yeah, but the problem is, William is already nearly using all of the OP quota to raise integers to 1t50 :smile:
Currently, OP is doing ECM somewhat faster than RSALS can sieve; but even 2t50 on the largest integers (SNFS difficulty above, say, 238-240) could tip the balance...

You may want to BOINCify ecm, as well. By the GIMPS pattern (TF, P-1, more TF, then LL) - when a number gets in the queue, it receives the lacking ECM treatment and then starts sieving.

[url]http://www.mersenneforum.org/showpost.php?p=234560&postcount=74[/url]

What does that increase the bound on odd perfect numbers to, and what's the next largest roadblock?

[QUOTE=fivemack;234561][URL]http://www.mersenneforum.org/showpost.php?p=234560&postcount=74[/URL]

What does that increase the bound on odd perfect numbers to, and what's the next largest roadblock?[/QUOTE]

According to [url]http://www.oddperfect.org/[/url] the next roadblock is sigma(2801^82) = C283.

Chris K

PS. Congratulations!

The Brent composite 593^89-1 had three previously known factors: 179, 169457, and 19121117. The C223 has been factored as P58 * P172.

ECM to t50 by yoyo@home
SNFS sieving by RSALS
Post Processing by Pace aka Zetaflux

Also, ECM factors were found for 149^103-1 and 43^137-1. These completed the goal of two known factors of at least 12 digits for these numbers.

[code]593^89-1
P58: 2840463295517967676236454436665384373463040823128761399097
P172: 6497271539685649825087455523739291301500686030129125736616629985162119696735251109574197171043740603003328835797022278156844709666378892370711139569369672279051099909501383

149^103-1
P41: 83300922286855977742998767417895549617459

43^137-1
P54: 138106407598771716757035804375653182925436330563197381
[/code]

My largest equal split to date:

[CODE]947_79_minus1
prp108 factor: 412162206264822345435611530468786989259988341878238149275963902235179375322643647900212611682048142360636743
prp108 factor: 602570462034741653744389923449493192747171483035727809190243541878294594097868404630738514951582650349235721
[/CODE]

Congratulations, neat!

Very nice split!

[QUOTE=Jeff Gilchrist;239652]My largest equal split to date:

[CODE]947_79_minus1
prp108 factor: 412162206264822345435611530468786989259988341878238149275963902235179375322643647900212611682048142360636743
prp108 factor: 602570462034741653744389923449493192747171483035727809190243541878294594097868404630738514951582650349235721
[/CODE][/QUOTE]

This reminds me of a cheerleader that I saw last night on TV.:smile: