Mersenneplustwo project.
Here is a record of the number, and size, of new factors found, as well as an indication of the total effort, for each year since 2005:
2005 - 10 (largest 38-digits) - 4GHz-yrs
2006 - 3 (largest 19-digits) - 12GHz-yrs
2007[so far] - 2 (largest 23-digits) - 100GHz-yrs
Friday, 7 December 2007
Thursday, 6 December 2007
M+2 progress
A bit of news from the Mersenneplustwo project:
As hoped for, getting Lenny the new MacBook going on those mid-range M+2's with mprime (ie by ECM) recently yielded a 21-digit factor from (M+2)1257787:
http://bearnol.is-a-geek.com/Mersenneplustwo/Mersenneplustwo.html
Thanks once again to George Woltman, for his cool software!
http://www.mersenne.org/freesoft.htm
This is the second new factor found this year (both by mprime)...
As hoped for, getting Lenny the new MacBook going on those mid-range M+2's with mprime (ie by ECM) recently yielded a 21-digit factor from (M+2)1257787:
http://bearnol.is-a-geek.com/Mersenneplustwo/Mersenneplustwo.html
Thanks once again to George Woltman, for his cool software!
http://www.mersenne.org/freesoft.htm
This is the second new factor found this year (both by mprime)...
Wednesday, 5 December 2007
Tuesday, 4 December 2007
FFTs-part5
The Cooley-Tukey Algorithm is an FFT algorithm especially suited, and adapted for large integer multiplication. It was first published in 1965.
GIMPS' mprime uses "radix-4" Cooley-Tukey to achieve a computation time of the order of NlogN (for N*N multiplication).
http://en.wikipedia.org/wiki/Cooley-Tukey_FFT_algorithm
GIMPS' mprime uses "radix-4" Cooley-Tukey to achieve a computation time of the order of NlogN (for N*N multiplication).
http://en.wikipedia.org/wiki/Cooley-Tukey_FFT_algorithm
Monday, 3 December 2007
FFTs-part4
Parseval's Theorem
A special case of Plancherel's Theorem, when function x = function y. Then the scaling constant = 1/(2*pi) [FT] or 1/N [DFT]
http://en.wikipedia.org/wiki/Parseval%27s_theorem
"The interpretation of this form of the theorem is that the total energy contained in a waveform x(t) summed across all of time t is equal to the total energy of the waveform's Fourier Transform X(f) summed across all of its frequency components f."
A special case of Plancherel's Theorem, when function x = function y. Then the scaling constant = 1/(2*pi) [FT] or 1/N [DFT]
http://en.wikipedia.org/wiki/Parseval%27s_theorem
"The interpretation of this form of the theorem is that the total energy contained in a waveform x(t) summed across all of time t is equal to the total energy of the waveform's Fourier Transform X(f) summed across all of its frequency components f."
Sunday, 2 December 2007
FFTs-part3
Plancherel's Theorem
A (unitary) relationship between the DFTs of any two functions x and y under multiplication (subject to a constant scaling factor), which property can be of additional use in simplifying the problem under computation.
http://en.wikipedia.org/wiki/Plancherel_theorem
A (unitary) relationship between the DFTs of any two functions x and y under multiplication (subject to a constant scaling factor), which property can be of additional use in simplifying the problem under computation.
http://en.wikipedia.org/wiki/Plancherel_theorem
Saturday, 1 December 2007
FFTs-part2
The DFT (discrete Fourier transform) is basically a digital sampling (ie approximation) of the analog Fourier transform, and as such it remains finite throughout the domain.
http://en.wikipedia.org/wiki/Discrete_Fourier_transform
A fast Fourier transform (FFT) is an efficient algorithm to compute the discrete Fourier transform and its inverse, for eg, a particular problem.
http://en.wikipedia.org/wiki/Fast_Fourier_transform
http://en.wikipedia.org/wiki/Discrete_Fourier_transform
A fast Fourier transform (FFT) is an efficient algorithm to compute the discrete Fourier transform and its inverse, for eg, a particular problem.
http://en.wikipedia.org/wiki/Fast_Fourier_transform
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