Fermat Prime search?

[siegert81]

Considering the massive increase in speed that GPUs enable, does anyone know if there's been an effort to test the "classical" Fermat numbers for primality?

F(33), F(34), F(35), F(40), F(41), F(44), F(45), F(46), F(47), F(49), F(50), F(51)...

These are all 2^2^N + 1, but no factors have been found, and primality tests have never been run.

Can GeneferCUDA be used to test these numbers?

[R.D. Silverman]

Originally Posted by siegert81

Considering the massive increase in speed that GPUs enable, does anyone know if there's been an effort to test the "classical" Fermat numbers for primality?

F(33), F(34), F(35), F(40), F(41), F(44), F(45), F(46), F(47), F(49), F(50), F(51)...

These are all 2^2^N + 1, but no factors have been found, and primality tests have never been run.

Can GeneferCUDA be used to test these numbers?

You are joking, right?

[c10ck3r]

Originally Posted by R.D. Silverman

You are joking, right?

Doubtful. Most likely he is ign'nt of GPU programs available and their applications.
Just my dos centavos.

[R.D. Silverman]

Originally Posted by c10ck3r

Doubtful. Most likely he is ign'nt of GPU programs available and their applications.
.

Knowledge of GPU programs is irrelevant.

[fivemack]

Originally Posted by R.D. Silverman

You are joking, right?

I don't think any current GPU has enough memory to do an FFT large enough to do p-1 or ECM on F33, but it's not in principle impossible; now that memory is cheap enough that people have 32G machines, p-1 or ECM in core on F33 or even F34 and F35 is feasible but hard. It looks as if FFTW out of the box can compute a 2^30-element FFT, which would be fine for F33.

Just checking potential factors would indeed be fairly straightforward on a GPU; probably need to write a little bit of new code because the factors are a bit bigger than for mersenne numbers, but computing 2^2^53 modulo (1..2^40)*2^51+1 wouldn't be that painful a job.

Obviously an LL test is impractical, but (being charitable, because it's always best to be charitable) trial factorisation with a couple-of-percent chance of proving compositude wouldn't be that onerous.

[rogue]

I suspect he is unaware of how much larger F(33) is than F(24).

[MattcAnderson]

The 24th Fermat number has 5,050,446 digits. The next smallest Fermat number of unknown character is F(33), which has 2,585,827,973 decimal digits. So Crandall and friends were able to determine primality of a number with just over five million digits. But F(33) has two and a half billion digits.

I have been working on fermat factors of the form k*2^36 + 1. There are no factors of this form for k < 10^16. Basically, I want to find a factor of the 34th Fermat number.

If someone were to write software that would do this search on a GPU, I would like that.

Matt

[R.D. Silverman]

Originally Posted by rogue

I suspect he is unaware of how much larger F(33) is than F(24).

Can't people do basic arithmetic? This is not a matter of knowing (say)
college level math. This is simple arithmetic.

[R.D. Silverman]

Originally Posted by fivemack

Just checking potential factors would indeed be fairly straightforward on a GPU; probably need to write a little bit of new code because the factors are a bit bigger than for mersenne numbers, but computing 2^2^53 modulo (1..2^40)*2^51+1 wouldn't be that painful a job.

Obviously an LL test is impractical, but (being charitable, because it's always best to be charitable) trial factorisation with a couple-of-percent chance of proving compositude wouldn't be that onerous.

It's been done. See, e.g. post #7

[msft]

Old my web page.

[firejuggler]

go there (fermatsearch) to get software dealing with fermat factors.