20030912, 11:33  #1 
Jun 2003
Russia, Novosibirsk
2×107 Posts 
79.300.000
I have simple questions and didn't see or missed(?) the answer to it in the forum.
So, as we know, there is an upper limit for exponents that is 79.300.000. First question is: why exactly is that number? Second: when will it be possible to wide that range, for example to 100.000.000 Third: does anyone works with exponents that is higher than 79.3E6? I made a program that can search for factors in the range of exponents of [0..100.000.000]. And I found about 60.000 factors to the Mnumbers that is higher than 2^79.3E6. If you are interested in that somehow, you are welcome to write here or directly to my email: hidden_warrior@mail.ru 
20030912, 11:59  #2 
Apr 2003
Berlin, Germany
551_{8} Posts 
The size of the maximal supported exponent depends on the max. implemented FFT size, how many bits you can put into each "digit" and floating point accuracy considerations.

20030912, 12:36  #3  
Aug 2002
2^{2}×3^{2}×5×47 Posts 
Glucas can go to 156,000,000...
Quote:


20030912, 13:36  #4 
Sep 2003
2585_{10} Posts 
For every range of exponents, the program uses an appropriate FFT size for its calculations. See for instance http://www.mersenne.org/status.htm (final column).
Exponents larger than 79.3M would require a larger FFT size, and the program code to implement that simply hasn't been written yet. Probably it will be in a few years when it becomes practical to test exponents in that range. 
20030912, 14:18  #5 
Jun 2003
Russia, Novosibirsk
2×107 Posts 
Thanks!
As my code for program doesn't use FFT I can expand the upper limit to higher numbers but my implementation of long arithmetics is not so fast as I would like it to be. I'll check GLucas to see what is that! Good luck! 
20031217, 20:01  #6  
"William"
May 2003
New Haven
943_{16} Posts 
Re: 79.300.000
Quote:
If either answer is "Yes," then Will Edgington would be interested in adding these factors (if they are new) to his data base of Mersenne Factors. See Will Edgington's Mersenne Page for more information. 
