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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 1110012 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

11100001101012 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 2·1,493 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.

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