79.300.000

HiddenWarrior · 2003-09-12, 11:33

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 M-numbers that is higher than 2^79.3E6. If you are interested in that somehow, you are welcome to write here or directly to my e-mail: hidden_warrior@mail.ru

Dresdenboy · 2003-09-12, 11:59

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.

Xyzzy · 2003-09-12, 12:36

Glucas can go to 156,000,000...

Quote:

4) The range of exponents has been doubled. Now Glucas can work with exponents up to 156000000. It will take a lot to complete this range :)

GP2 · 2003-09-12, 13:36

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.

HiddenWarrior · 2003-09-12, 14:18

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!

wblipp · 2003-12-17, 20:01

Quote:

Originally posted by HiddenWarrior
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 M-numbers that is higher than 2^79.3E6.

Are these factor for prime exponents? If composite exponents, are they factors of the primitive part? (Mersennes with composite exponents have smaller Mersennes as factors. A factor of the primitive part is not a factor any of these smaller Mersenne numbers).

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.

2003-09-12, 11:33	#1
HiddenWarrior Jun 2003 Russia, Novosibirsk 326₈ 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 M-numbers that is higher than 2^79.3E6. If you are interested in that somehow, you are welcome to write here or directly to my e-mail: hidden_warrior@mail.ru

2003-09-12, 11:59	#2
Dresdenboy Apr 2003 Berlin, Germany 169₁₆ 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.

2003-09-12, 13:36	#4
GP2 Sep 2003 5×11×47 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.

2003-09-12, 14:18	#5
HiddenWarrior 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!