About M1277

[VBCurtis]

My source for 3* t65 is Ryan's post here:
https://mersenneforum.org/showpost.p...5&postcount=57

Where he believes he completed a t70 over a year ago.
3* t65 is about half a t70, so I was being conservative with my "guarantee", since I figure if Ryan thinks he did a t70 he surely finished half of one at minimum (plus all the other ECM work that everyone else has done, which might be close to a T65 by now).

[chalsall]

Originally Posted by kriesel

With such a cordial invitation from VBCurtis, how could anyone resist.

Clearly, you couldn't. And I thank you for that. Sincerely.

While a bit "lengthy", it sums things up nicely and understandably for the layperson (of which I am in this domain).

IMO, this on par to an Economist (the newspaper) article.

As in, deeply researched, well thought, and clearly argued.

[charybdis]

Originally Posted by kriesel

(What is t65?)

t65 = expected amount of ECM effort to find a 65-digit factor, if one exists. See here for the actual curve counts.

I estimate the indicated effort already expended corresponds to ~3900. CPU-core-years.

This is way off. I'd be surprised if it was even 10% of this. Don't forget that GHz-days will be a big overestimate because they assume stage 2 is done by Prime95, not GMP-ECM which is much faster.
Exercise for the reader: run a single curve at B1=29e8, using GMP-ECM for stage 2; then multiply the time taken by 115153 to estimate the total CPU-time for Ryan's t70, which probably makes up at least 50% of the total ECM done on M1277.

[kriesel]

Originally Posted by charybdis

This is way off.

Including Ryan Propper's t65 and t70?

[charybdis]

Originally Posted by kriesel

Including Ryan Propper's t65 and t70?

Yes, that was the whole point of suggesting that the reader (i.e. you) run a curve at the t70 level and use that to estimate the time required for a full t70.
Hint: the time for such a curve is measured in hours. Not days.

[SethTro]

Originally Posted by VBCurtis

Anyone who considers TF on M1277 is assigned the task of determining how much ECM has been run, as it applies to the chances of a factor remaining below some bit level far far out of reach of TF- say, 100 bits.

I guarantee that more than 3 * t65 of ECM has been run. Given this, what are the odds of a factor below 100 bits? 120 bits? 150 bits?

The only correct answer to any commentary pondering TF on M1277 is "you are wasting your time". But Ken likes to write essays about such things, so perhaps he will do so for this assignment as well.

We already did the math in another post: https://www.mersenneforum.org/showthread.php?t=23280 starting around #60

Re-running my numbers I get a slightly different result (using Dickman's function

t65 - t70: 6%
t70 - t75: 6.6%
t75 - t80: 7.3%

Assuming Ryan has completed most of t70 / t75 we'll see maybe 10% probability of an ECM factor over the next ~10 years assuming GPUs get faster...

[mathwiz]

All this talk of fuzz testing weird/nonstandard inputs to GMP-ECM (including kriesel's essays) should be moved to another thread. This thread is about factoring M1277.

[masser]

Originally Posted by mathwiz

All this talk of fuzz testing weird/nonstandard inputs to GMP-ECM (including kriesel's essays) should be moved to another thread. This thread is about factoring M1277.

Done. Please see this thread for the very manly (i.e. idiotic with a lot of posturing) discussion of how to use GMP-ECM.

[masser]

Originally Posted by BigNumberGuy

[NEWCOMER ALERT]
I was messing around in mersenne.ca and saw that M1277 was the smallest composite number with no factor, and all of TF, P-1 and ECM had been done to a high degree.
Is it likely that we will factor M1277 in the next, say, 5-10 years? what about 20 years?

Here's a link to the group effort factorization of M991. I'm not sure how the community decided (some discussion here) it was time to tackle that particular exponent, but once they did the effort took about 7 months (November 2014 to June 2015). Very cool!

Here's the M947 effort, too!

[VBCurtis]

Interested potential-factorers / readers may want to review the previous M1277-factoring thread: https://www.mersenneforum.org/showthread.php?t=23280

[BigNumberGuy]

first off hang on where the heck did like 5 pages of responses go?
second, this isnt related (i dont feel like a new thread) but why doesn't mprime (Mac) use up 100% of the cpu? I thought it was designed to do that??