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2018-03-07, 18:54   #452
Dubslow

"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

3·29·83 Posts

Quote:
 Originally Posted by Brownfox My approximation for cofactors with 90-110 digits is as follows: Number of factors other than 2 or 3 Expectation (%)
Quote:
 Originally Posted by Dubslow ...So the overall odds of getting a 3^2 is m/(3*2^m), while the overall odds of getting any even power of 3 is m/(2^m*(3 + 27 + 243 + ...)) = 3m/2^(m+3) (since 1/(3+27+243+...) = 3/8).
Using your distribution for m (obviously subject to the same warning about sample size) together with the half-assed theory, I came up with the following theoretical approximation:

Code:
In [2]: m_dist = [.014, .028, .138, .244, .235, .157, .088, .060, .023, .009, .005]

In [3]: def odds_of_even_3(m): return 3*m/(2**(m+3))

In [8]: def total_odds_even_3(m_dist):
...:     from math import fsum
...:     return fsum(odds_of_even_3(m)*odds_m for m, odds_m in enumerate(m_dist, 1))

In [9]: total_odds_even_3(m_dist)
Out[9]: 0.07214776611328125
This compares to

Quote:
 Originally Posted by Brownfox Chance of getting to an even power of 3 is 0.024
Which is not bad, off by (almost exactly) a factor of 3, and half an order of magnitude is about all I could have hoped for going into it.

 2018-03-07, 19:00 #453 Dubslow Basketry That Evening!     "Bunslow the Bold" Jun 2011 40
 2018-03-07, 19:05 #454 Brownfox     Dec 2017 3·19 Posts All primes to any power. Note that the vast majority are not to a non-unit power. Regards Steve
2018-03-07, 20:08   #455
Dubslow

"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

1C3516 Posts

Quote:
 Originally Posted by Brownfox All primes to any power. Note that the vast majority are not to a non-unit power. Regards Steve
Hmm, I think that means my number is an underestimate then, since it's overcounting the m for my purposes, and higher m = lower odds.

 2018-03-27, 00:10 #456 RichD     Sep 2008 Kansas 31·97 Posts C192 @ i1685 As a placeholder of work completed, yoyo has finished a full t55 on this number. When interest resurfaces at a later time, I believe only a t60 will be needed before moving to a NFS job.
2020-07-13, 15:59   #457
swellman

Jun 2012

2×17×83 Posts

Quote:
 Originally Posted by RichD As a placeholder of work completed, yoyo has finished a full t55 on this number. When interest resurfaces at a later time, I believe only a t60 will be needed before moving to a NFS job.
Yoyo@Home just finished up ECM to t60. It is ready for NFS whenever someone is game.

Maybe Ryan will take an interest.

 2020-07-13, 22:01 #458 VBCurtis     "Curtis" Feb 2005 Riverside, CA 5×7×112 Posts I'll do some poly select this week; this is a small enough job that I can do the CADO select solo. I'll wait till Tuesday evening or Wed to get started, in case Ryan reserves the job. If someone else wants to poly select anyway, let me know and I'll post my settings so we don't overlap.

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