CPU time for 100M digit prime test

[biggerben]

Hi all,

Apologies if I just couldn't find this in some FAQ -- but I can't find it.
How long would it take to test a 100M digit mersenne prime on a modern computer?
How many exponents could I test at the same time on an intel i7?
Are there any estimates for the likelyhood of a 100M digit mersenne number being prime?

I'm thinking of joining the 100M digit prime hunt but am surprised by the lack of information. But then again maybe I'm just looking in the wrong places :)

[kladner]

Uncwilly, or someone he knows of, is most likely to have your answers

[retina]

It could take anything from a few months to 37 years. The runtime depends depends upon many many factors.

[Uncwilly]

Originally Posted by retina

It could take anything from a few months to 37 years. The runtime depends depends upon many many factors.

The link is your quick easy bet. Or use James H.'s website.

The likelihood is very, very low.
Some would suggest that you do a 'shakedown' run of 2 or 3 double checks (per core) first. That way you will know that the machine is stable.

Running all of the cores on a single number might be best for exponents that high at the moment. The longer (clock/wall time) that the test takes, the greater the likelihood of random errors. Running all cores on a single exponent will result in few exponents per year, but I think that might be off set by the fewer errors.

Make sure you are using the 64 bit version of Prime95, if your OS is 64 bit too.

[TheMawn]

Originally Posted by biggerben

Hi all,

How long would it take to test a 100M digit mersenne prime on a modern computer?
How many exponents could I test at the same time on an intel i7?

I'm thinking of joining the 100M digit prime hunt but am surprised by the lack of information. But then again maybe I'm just looking in the wrong places :)

A test for M_P = 2^P - 1 uses M_P itself at every iteration and runs P - 2 iterations, which makes the test very roughly O(n²) which is fancy math lingo for quadrupling the run time for doubling the exponent size. By increasing the exponent, you increase the difficulty of the iteration AND the number of iterations, so you're getting a double-whammy.

For example, look at a CPU benchmark page for the i7-4770K.

M25,525,000 takes 6 milliseconds per iteration and M50,275,000 takes 12 milliseconds per iteration, and there's twice as many iterations, so you can see the "quadrupling".

100M digits happens around M333,000,000. This exponent is roughly eight times the size of M41,280,000 which means the iterations are roughly eight times longer (so 80 ms). 333,000,000 iterations at 80 ms/iteration gives 309 days.


You can run as many tests as you have physical cores on your CPU. The i7-4770K has four physical cores (also four logical cores, but they don't help) so you can choose between 4 tests or 1 test using all four cores, which is faster but makes less efficient use of the CPU.

[kladner]

There is a commonly expressed opinion that such lengthy assignments should be run with ECC RAM.

[retina]

Originally Posted by TheMawn

The i7-4770K has four physical cores (also four logical cores, but they don't help)...

Not really. It has 4 physical execution cores, yes. But it has 8 logical cores feeding those 4 physical cores.

But you can't add them together and pretend it is 12 cores.

[Lorenzo]

See these thread http://www.mersenneforum.org/showthread.php?t=13185