Suggestions for a new Prime95 version

[joblack]

In the readme.txt of prime95 v29b it is stated that:

* "The Test choice can be used to run a Lucas-Lehmer test on one Mersenne
number. Enter the Mersenne number's exponent - this must be a prime
number between 5 and 560000000".
Is the border of 560000000 an artificial or a technical one? How about giving people with 'monster hardware' the chance of playing with higher numbers.

* In the Advanced - Test ... menu it is possible to insert a prime number. An interesting feature would be a slider to slide through the possible prime numbers for n.

Additionally it would be fine to step from one prime number to the next (for instance: if one is taken). That could be possible with arrow buttons for the next prime number (at the moment I have to print out the prime number range externally or try out until the program approves the input).

Greetz
jb

[jrk]

I would guess the reason 560M is the limit is because the software doesn't have any FFT code to handle larger exponents.

But remember, doing a LL of a mersenne with exponent around 560M is about 200 times as hard as doing a LL on exponents currently being assigned around 40M. And you're much more likely to find a mersenne prime if you do 200 exponents around 40M than if you do only one at 560M. So I don't think there is much pressure to change the limits.

I could be wrong in my assessment, though.

[joblack]

Originally Posted by jrk

I would guess the reason 560M is the limit is because the software doesn't have any FFT code to handle larger exponents.

But remember, doing a LL of a mersenne with exponent around 560M is about 200 times as hard as doing a LL on exponents currently being assigned around 40M. And you're much more likely to find a mersenne prime if you do 200 exponents around 40M than if you do only one at 560M. So I don't think there is much pressure to change the limits.

I could be wrong in my assessment, though.

I don´t think it would take 200 times as long. I tried to highest possible 560M mersenne prime numbers. Somebody is already trying this and the time estimation isn´t that much longer than a 100M (around 5 x longer I suppose).

[garo]

It is much more that 5.6 times longer as you will have to use a bigger FFT size which would mean slower iterations. Just put in a test line in your worktodo and see the completion date.

[joblack]

Originally Posted by garo

It is much more that 5.6 times longer as you will have to use a bigger FFT size which would mean slower iterations. Just put in a test line in your worktodo and see the completion date.

Nov 2019 - that means 11 years.

For a 100M number I need around 2 - 3 years.
---

I tried it out:

*****************************
[Comm thread Jan 5 13:22] PrimeNet error 40: No assignment
[Comm thread Jan 5 13:22] ra: redundant LL effort, exponent: 560000011
[Comm thread Jan 5 13:22] Registering assignment: LL M559999987
[Comm thread Jan 5 13:22] URL: http://v5.mersenne.org/v5server/?v=0...0&p1=0&ss=6334
[Comm thread Jan 5 13:22] RESPONSE:
[Comm thread Jan 5 13:22] pnErrorResult=40
[Comm thread Jan 5 13:22] pnErrorDetail=ra: redundant LL effort, exponent: 559999987
[Comm thread Jan 5 13:22] ==END==
[Comm thread Jan 5 13:22]
[Comm thread Jan 5 13:22] PrimeNet error 40: No assignment
[Comm thread Jan 5 13:22] ra: redundant LL effort, exponent: 559999987
[Comm thread Jan 5 13:22] Done communicating with server.
*****************************

Does that redundant LL effort mean that there are already people working on that? Additionally it seems to work to test higher exp. than 560M.

http://v5www.mersenne.org/primenet/

shows exponents up to 999M, but nobody working on the +/- 560M range ...

[S485122]

Originally Posted by joblack

I tried it out:
...
[Comm thread Jan 5 13:22] ra: redundant LL effort, exponent: 560000011
...
[Comm thread Jan 5 13:22] ra: redundant LL effort, exponent: 559999987
...
Does that redundant LL effort mean that there are already people working on that?
...

It means that you choose exponents that have already been factored.

Try 559999897 and 560000039...

Jacob

[S485122]

I timed 560000039 on core2 Quad at 2940 MHz :
One thread would take 14 years and 10 month.
Four threads would take 5 yeas and 5 month.

This would also mean that numbers bigger than 560M can be tested...

Jacob

[jrk]

Originally Posted by joblack

I don´t think it would take 200 times as long. I tried to highest possible 560M mersenne prime numbers. Somebody is already trying this and the time estimation isn´t that much longer than a 100M (around 5 x longer I suppose).

Now remember I said it would take 200 times as long as a 40M test (those currently being assigned), not 200 times as long as a 100M test.

But here is how you can figure it yourself:

The test time is proportional to both the iteration time and iteration count.

The iteration time is proportional to the FFT size that the test will use. The FFT size increases roughly linearly with exponent p (actually the FFT size increments in steps, but for our purposes here that isn't very important).

The iteration count is p-2.

So roughly speaking, the test time will be proportionally about p^2.

If a 40M exponent takes X days, then a 560M exponent will take ~196*X days. Since 560^2 / 40^2 = 196.

[joblack]

Originally Posted by S485122

I timed 560000039 on core2 Quad at 2940 MHz :
One thread would take 14 years and 10 month.
Four threads would take 5 yeas and 5 month.

This would also mean that numbers bigger than 560M can be tested...

Jacob

I have some other calculations - 4 threads (also a quad core - same clocking) would take 14 years ... try out prime v28 or v29 - that seems to be more accurate in the estimation

Now I get the

********************************[Main thread Jan 5 21:34] Mersenne number primality test program version 25.9
[Comm thread Jan 5 21:34] Registering assignment: LL M560000039
[Comm thread Jan 5 21:34] URL: http://v5.mersenne.org/v5server/?v=0...0&p1=0&ss=5523
[Comm thread Jan 5 21:34] RESPONSE:
[Comm thread Jan 5 21:34] pnErrorResult=40
[Comm thread Jan 5 21:34] pnErrorDetail=ra: already assigned, exponent: 560000039, A: 1, b: 2, c: -1
[Comm thread Jan 5 21:34] ==END==
[Comm thread Jan 5 21:34]
[Comm thread Jan 5 21:34] PrimeNet error 40: No assignment
[Comm thread Jan 5 21:34] ra: already assigned, exponent: 560000039, A: 1, b: 2, c: -1
[Comm thread Jan 5 21:34] Done communicating with server.
[Main thread Jan 5 21:34] Starting workers.
*************************************
But some hours ago it worked perfect (no error message). I think the 'already assigned' algomrithm doesn´t work that good on server and/or client side ... perhaps a job for the prime95 user ...

[S485122]

Originally Posted by joblack

I have some other calculations - 4 threads (also a quad core - same clocking) would take 14 years ... try out prime v28 or v29 - that seems to be more accurate in the estimation

I used Prime95 v25.9.1 for those calculations. But if you use the Advanced / Test instead of the Advanced / Time option, you assign the exponent to your self and in the Status there is a maximum date if I remember correctly.

Originally Posted by joblack

Now I get the
[Comm thread Jan 5 21:34] ra: already assigned, exponent: 560000039, A: 1, b: 2, c: -1

But some hours ago it worked perfect (no error message). I think the 'already assigned' algomrithm doesn´t work that good on server and/or client side ... perhaps a job for the prime95 user ...

I you checked via "Result Queries" / "Exponent Status" you would see the exponent is already assigned to you as a concequence of your using the Test option instead of the Time option :
"560000039 No factors below 2^59
Assigned LL testing to "joblack" on 2009-01-05"

Jacob

[joblack]

Originally Posted by S485122

I used Prime95 v25.9.1 for those calculations. But if you use the Advanced / Test instead of the Advanced / Time option, you assign the exponent to your self and in the Status there is a maximum date if I remember correctly.I you checked via "Result Queries" / "Exponent Status" you would see the exponent is already assigned to you as a concequence of your using the Test option instead of the Time option :
"560000039 No factors below 2^59
Assigned LL testing to "joblack" on 2009-01-05"

Jacob

Yep you´re right. So Prime95 doesn´t recognize if I already started testing it?