Re: Prime chains x-->Ax+B [puzzle 2]

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• ... Some way back, you reported using a wheel of size 510510 = 17# and you reported the factorization ... In such a case,
Message 1 of 143 , Jan 4, 2011
Kevin Acres <research@...> wrote:

> A review of logs of 14+ chains gives me 17 15/16 amongst 226 14/16.
> Some of these are outside of my preferred x < 51561510 search area,
> where the yield of 15/16 becomes somewhat less.

Some way back, you reported using a wheel of size 510510 = 17#
and you reported the factorization
> [16, 3052362829787719304602274593,
> [43, 1; 80048363, 1; 886778685131718377, 1]]

In such a case,

prod(p=2,17,1-isprime(p)/p)*log(3052362829787719304602274593) =~ 11.4

estimates the mean number of 15's that you might need for a 16.

By my reckoning you now have about 23 runs of 15.
The a priori probability of a 16th prime was about
1 - exp(-23/11.4) = 87%
so it appears that you have been unlucky.

David
• ... Suppose that we want to start with a square and get a square. Then we must solve the Diophantine equation y^2 = a*x^2 + b For any pair (a,b), Dario will
Message 143 of 143 , Jan 7, 2011