Tables need effort

[dantringuoi]

I was trying to figure out if it was worth the effort to certify a prime and I wondered if there was a table somewhere showing the expected effort needed to do so with some program(s).

Come to think of it, this would be useful for a lot of other things as well -- effort needed to find a factor of a given size with ECM, effort needed to crack a composite with NFS, etc.

Does anyone know of a resource like that? Even just a thread?

Lee

Tks!!

[VBCurtis]

Cracking with GNFS is simple- time your rig for a small number like a C100, and then difficulty doubles every 5 to 5.5 digits.

Timing varies so much from machine to machine that it's vastly more accurate to run a C100 yourself than it is to trust someone else's timings. I can say that numbers under C130 can be cracked by even the impatient, while C155+ takes either some patience (like a week at 155 digits) or a fairly powerful rig.

Primality proving via LLR for the usual special forms has difficulty increasing with the square of the exponent- again, run a small test like a 100k exponent, and extrapolate. Timings of a small top-5000 number are an hour or less, a million decimal-digit number 2-4 single-thread hours.

Generating a primality certificate with e.g. Primo for a number of no special form is something I don't know the scaling for- surely someone with experience will chime in!

Edit: For ecm, just use ecm -v to get a chart of # of curves vs factor size, and calculate your own. Again, so much variance from machine to machine (not to mention that often there isn't a factor to be found- so one has to be specific about time to run a t40 or t45 versus the time to actually find a factor in a given list of numbers, or some other goal)

[paulunderwood]

Originally Posted by VBCurtis

.

Generating a primality certificate with e.g. Primo for a number of no special form is something I don't know the scaling for- surely someone with experience will chime in!

ECPP is O(ln(n)^(4+eps)) meaning a doubling in length takes 16 times as long. This can be helped by having a many-core system.

It took me 21.5 months to certify a 40000 digit number on a 48 core 2.3Ghz Opteron system. If you have time on a AMD 3990x you will be laughing!

[a1call]

Originally Posted by paulunderwood

If you have time on a AMD 3990x you will be laughing!

Probably not all the way to the bank.

https://www.amazon.com/AMD-Ryzen-Thr...1350078&sr=8-4

But thanks for the info. I was looking for a multi thread computer.
Now if I could only justify the cost. Presently I have cut back on my prime-number-crunching because I am afraid to overheat my systems which I am relying on for telecommuting. It won't be easy/safe to replace them with current pandemic in place.
BTW you had the top record in the world for quite some time my friend, so don't sell your system too short.

[paulunderwood]

Originally Posted by a1call

Probably not all the way to the bank.

https://www.amazon.com/AMD-Ryzen-Thr...1350078&sr=8-4

But thanks for the info. I was looking for a multi thread computer.
Now if I could only justify the cost. Presently I have cut back on my prime-number-crunching because I am afraid to overheat my systems which I am relying on for telecommuting. It won't be easy/safe to replace them with current pandemic in place.
BTW you had the top record in the world for quite some time my friend, so don't sell your system too short.

A 3990x will necessary to certify R49081 in a timely manner when Marcel upgrades Primo.

As for my Opteron System: It stopped working and the good parts will be sold on eBay soon.