## Proth coefficients & weights

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• ... Thank you for the congrats, Pavlos. Indeed, of the seven PCs available to me, three of them are spending all of their idle time looking for primes of the
Message 1 of 2 , Feb 19, 2001
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--- In primenumbers@y..., "Pavlos S." <pavlos119@y...> wrote:

> Congratulations to g42 for the new and amazing prime:
> 577294575*2^223519+1.It seems that this specific k
> produces a great many primes.And also g42 has been
> patient enough to seek in higher limits!Can anyone
> tell me what the probability is that a
> 10-million-digit prime of the form 577294575*2^n+1
> exists that can be discovered by proth(i.e
> 33219000<n<33554000)?

Thank you for the congrats, Pavlos. Indeed, of the seven PCs
available to me, three of them are spending all of their idle
time looking for primes of the form 577294575*2^n+1.

probability that a prime of the form 577294575*2^n+1 would be
found with 33219000<n<33554000.

Just to discourage you from even trying, let me give you some
raw numbers. I'm currently (in the n ~ 225000 range) expecting
to find a new prime roughly every 100 CPU days. The amount of
time expected to find primes is generally O(log(N)^3) -- see
the explanation of production scores at:

http://www.utm.edu/research/primes/bios/TopCodes.html

150 times greater than log(N) for my range, so primes will take
about 150^3 times longer to find... you'll expect to find a
new prime roughly every 100*150^3 CPU days -- once every million
CPU years!

Given the number of tractable problems in computational math,
it would be a shame to waste CPU cycles on such an impossible
long shot. Offer some help with the Cunningham table projects,
or finish computing the aliquot sequence starting at 276, or
look for a Cunningham chain of length 20; you might even try
to find an odd perfect number, or raise the lower bound for such
numbers -- in my opinion, the discoverer of the first odd
perfect number (if one exists) will be more famous than any
discoverer of primes. But, that's just my opinion.

Jack Brennen
"g42"
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