I'm not sure that this is the right place for this, given that the exponent is composite, but...

M1369 has a factor: 6337549872222510181433065176903666450905719.

The cofactor, (after dividing out this and the previously known algebraic and non-algebraic factors) is a PRP349, which completes the factorisation of this exponent.

Found by ecm stage 2. sigma=2257798857, B1=43000000, B2=default.

Group Order: 2^3 · 3^2 · 17 · 457 · 15901 · 44449 · 88897 · 543611 · 6754669 · 49108642183

Before I found the factor, I had been thinking that I would probably not see the exponent fully factored in my lifetime. My reasoning was that it was about a billion times harder than the largest SNFS job so far completed. (I'm 48 years old. I don't have time for Moore's law to catch up.) The exponent was low, so probably already had been subject to a lot of ECM, and even finding one or two small factors would not reduce the GNFS difficulty below the SNFS difficulty.

I concluded that my best hope was to find a small factor and discover that the cofactor was prime. I did not think this was likely. Nevertheless I was prepared to take the number up to t50, which I figured I could do in about a month or less using one core. In the end, it only took a few hours.

So, this time , luck was the determinant factor.

Wowzers. That was incredibly lucky!

[QUOTE=Mr. P-1;328837]In the end, it only took a few hours.[/QUOTE]

Wish they were all like that!

Woohaaa! Congrats! Nice finding.

[QUOTE=Mr. P-1;328837]I'm not sure that this is the right place for this, given that the exponent is composite, but...

M1369 has a factor: 6337549872222510181433065176903666450905719.

The cofactor, (after dividing out this and the previously known algebraic and non-algebraic factors) is a PRP349, which completes the factorisation of this exponent.

Found by ecm stage 2. sigma=2257798857, B1=43000000, B2=default.

Group Order: 2^3 · 3^2 · 17 · 457 · 15901 · 44449 · 88897 · 543611 · 6754669 · 49108642183
[/QUOTE]
[EMAIL="ssw@cerias.purdue.edu"]Send e-mail to Sam Wagstaff[/EMAIL] ; he has [URL="http://homes.cerias.purdue.edu/~ssw/cun/xtend/index.html"]extension[/URL] pages.
Congrats!

[QUOTE=flashjh;328895]Wish they were all like that![/QUOTE]

If they were, then they would all have been found by now.

[QUOTE=Dubslow;328877]Wowzers. That was incredibly lucky![/QUOTE]

Lucky in what sense? Lucky that there was a P43 waiting to be found? That depends upon how much ECM other people had done before me. If, as I had assumed, it was "a lot", then, then it's more a case that these other searchers had been unlucky. On the other hand, my success might suggest that there is still a lot of low-hanging fruit among the composite-exponent near-Cunninghams. (Perhaps also the prime-exponents other than 2-.)

If you meant lucky to find the factor so quickly, the expected time to t40 was about a day or so for a single core on my machine. I found the P43 in a few hours. Lucky, but not incredibly so.

[QUOTE=Batalov;328918][EMAIL="ssw@cerias.purdue.edu"]Send e-mail to Sam Wagstaff[/EMAIL] ; he has [URL="http://homes.cerias.purdue.edu/~ssw/cun/xtend/index.html"]extension[/URL] pages.
Congrats![/QUOTE]

Sent. Also to Will Edgingon.

[QUOTE=Mr. P-1;328837]The cofactor, (after dividing out this and the previously known algebraic and non-algebraic factors) is a PRP349[/QUOTE]

Now [url=http://factordb.com/index.php?id=1100000000584435267]confirmed[/url] as a P.

P-1 found a factor in stage #2, B1=580000, B2=10730000.
UID: Jwb52z/Clay, M61367717 has a factor: 81843081338400211462447

76.115 bits

M89576251 has a factor: 391226059433524759463 (68.4 bits)
k = 701 * 3,115,206,781.