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Old 2015-10-17, 21:24   #5
ewmayer's Avatar
Sep 2002
Rep├║blica de California

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The prime-odds have just been raised! (Actually the odds remain the same, it is my estimate thereof which has increased.)

Originally Posted by ewmayer View Post
3. The factorizations of the remaining not-div-by-3 terms appear to be 'random', i.e. modelable by the statistics of randomly chosen odd integers of similar size.
That statement neglects that by construction, the remaining terms are not divisible by 3 or 5, i.e. if the factorization is indeed random (or at least random as far as aggregate odds are concerned), it is so primes > 5. Thus my Pari-loop estimates all need to multiplied by (3/2)*(5/4) = 15/8, i.e. are nearly doubled.

Of course those are the naive odds - the conditional odds given no primes found below 10^5 are still quite low for the 10^5 - 10^6 range, around 10%.

Last fiddled with by ewmayer on 2015-10-17 at 21:26
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