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Old 2018-03-07, 18:54   #452
Dubslow
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40<A<43 -89<O<-88

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Quote:
Originally Posted by Brownfox View Post
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 View Post
...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 View Post
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.
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Old 2018-03-07, 19:00   #453
Dubslow
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40<A<43 -89<O<-88

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Actually, now I know for certain that no one read my previous theory post, because it's got some horrifically wrong notation that any middle schooler with algebra should be able to point out.

Specifically, 1/x + 1/y does not equal 1/(x+y).

I'm still pretty sure the final result is "correct" (I was doing the right math in my head, even if what I wrote down is god-awfully wrong), but the last few expressions before that final result are blasphemy before my algebra teachers. So, sorry....

Last fiddled with by Dubslow on 2018-03-07 at 19:01
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Old 2018-03-07, 19:05   #454
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All primes to any power. Note that the vast majority are not to a non-unit power.

Regards
Steve
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Old 2018-03-07, 20:08   #455
Dubslow
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40<A<43 -89<O<-88

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Quote:
Originally Posted by Brownfox View Post
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.
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Old 2018-03-27, 00:10   #456
RichD
 
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Default 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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