20050405, 18:08  #1 
Apr 2005
26_{16} 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. 
20050405, 18:16  #2  
Banned
"Luigi"
Aug 2002
Team Italia
12EC_{16} Posts 
Quote:
Luigi 

20050405, 21:17  #3 
Jul 2004
Nowhere
809 Posts 
welcome everyone to welcome Vijay i have made 3 yes 3 danceing bannas

20050405, 21:38  #4 
"Kyle"
Feb 2005
Somewhere near M52..
3·5·61 Posts 
Welcome Vijay!

20050406, 07:34  #5 
Jan 2005
Singapore
13 Posts 
Welcome ! The more the merrier

20050406, 08:21  #6 
Bronze Medalist
Jan 2004
Mumbai,India
2052_{10} Posts 
Hello I'm new to discovering Mersenne primes
Welcome Vijay! Nice to see a familiar name.
We wont let you down Mally 
20050406, 11:23  #7 
Apr 2005
46_{8} 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 
20050406, 13:19  #8  
Nov 2003
2^{2}×5×373 Posts 
Quote:
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 EulerMascheroni 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^p1 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. 

20050406, 15:01  #9 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×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 
20050406, 19:38  #10 
Apr 2005
2×19 Posts 
I see...
Ok, so by the equation you feel that it will take time finding the next prime (<<That rhymes!)
But the thing is, its not too long before you'll see some kind of patterns emerging in the mersenne exponents. The cumbersome way of trying to find primes by testing each exponents, will be replaced by an equation that will calculate the exponent itself. I just know it! Currently, I'm working on calculating the face of God by integrals 
20050406, 19:41  #11 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
So, does god converge?
Alex 
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