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 2005-04-05, 18:08 #1 Vijay   Apr 2005 2616 Posts Hello, I'm new to discovering Mersenne primes Hello, I've only just joined mersenne.org to help discover further mersenne primes, as I felt my computer to be quite powerful and it seemed it needed exercise. Personally I'm a mathematician.
2005-04-05, 18:16   #2
ET_
Banned

"Luigi"
Aug 2002
Team Italia

12EC16 Posts

Quote:
 Originally Posted by Vijay Hello, I've only just joined mersenne.org to help discover further mersenne primes, as I felt my computer to be quite powerful and it seemed it needed exercise. Personally I'm a mathematician.
Welcome to the group, Vijay!

Luigi

 2005-04-05, 21:17 #3 moo     Jul 2004 Nowhere 809 Posts welcome everyone to welcome Vijay i have made 3 yes 3 danceing bannas
 2005-04-05, 21:38 #4 Primeinator     "Kyle" Feb 2005 Somewhere near M52.. 3·5·61 Posts Welcome Vijay!
 2005-04-06, 07:34 #5 blackguard   Jan 2005 Singapore 13 Posts Welcome ! The more the merrier
 2005-04-06, 08:21 #6 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 205210 Posts Hello I'm new to discovering Mersenne primes Welcome Vijay! Nice to see a familiar name. We wont let you down Mally
 2005-04-06, 11:23 #7 Vijay   Apr 2005 468 Posts Hello Everyone! Thank you for a warm welcome everyone! I'm sure with our raising computer power, the next M prime is not to far before it is uncovered
2005-04-06, 13:19   #8
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by Vijay Thank you for a warm welcome everyone! I'm sure with our raising computer power, the next M prime is not to far before it is uncovered
Not quite.

Although a proof is lacking, there are heuristical arguments to suggest
that the number of Mersenne primes between 2^n and 2^(2n) should
be (asymptotically) exp(gamma), where gamma is the Euler-Mascheroni
constant. i.e. there should be a little more than one Mersenne prime
in the exponent range from n to 2n, independent of n [on AVERAGE]

Each Mersenne prime test on M_p = 2^p-1 requires p multiplications mod
M_p. Each multiplication takes time O(p log p loglog p) via a weighted
discrete Fourier Transform. Thus, each test requires O(p^2 log p loglog p)
work. Given a newly discovered Mersenne prime M_p, the *expected*
work to then find the next one is

O( integral from p to 2p of x^2 log x loglog x dx)

For sufficiently large x we have:

O(x^2 log x loglog x) ~ x^(2+o(1))

Thus, the above integral can be approximated by:

int from p to 2p of x^(2 + o(1)) dx and this is at least 8 times the
work to find the previous Mersenne prime.

This project has been very lucky in its last two successes. We should expect
that every new Mersenne prime we find will be "roughly" an order of magnitude harder than the previous one.

 2005-04-06, 15:01 #9 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 22×33×19 Posts Hello I'm new to discovering Mersenne primes [QUOTE=R.D. Silverman]Not quite. WoW Bob! that was a great introduction. Please keep it up. Mally
 2005-04-06, 19:38 #10 Vijay   Apr 2005 2×19 Posts I see... Ok, so by the equation you feel that it will take time finding the next prime (<
 2005-04-06, 19:41 #11 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts So, does god converge? Alex

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