Question: PRP and LLR
 

I'm still a noob (with lots of computing power) at this prime stuff. I'm just curious, what is the difference between proth.exe (PRP) and LLR.exe (LLR)?

I'm just messing around checking out how they work, and I don't know what the difference is between the two. If I was to be looking for a standard k*2^n-1 prime, what program would be the choice? Thanks for any info!

Basically, the difference is:
LLR gives you a definite answer: (1) this number is prime or (2) it isn't.
PRP can say: (1) this number is definitely composite, or (2) this number is probably prime, but there are still chances that it isn't.

[QUOTE=gribozavr;100333]Basically, the difference is:
LLR gives you a definite answer: (1) this number is prime or (2) it isn't.
PRP can say: (1) this number is definitely composite, or (2) this number is probably prime, but there are still chances that it isn't.[/QUOTE]

Note that Yves Gallot's Proth.exe ALSO gives a definite answer! Not to be confused with George Woltman's PRP, which is a probable prime asserting program (but which is very fast).

[QUOTE=Jean Penné;100339]Note that Yves Gallot's Proth.exe ALSO gives a definite answer! Not to be confused with George Woltman's PRP, which is a probable prime asserting program (but which is very fast).[/QUOTE]
Also, both PRP and LLR are much faster than Gallot's Proth.exe. For n=195,000, I needed about 5 minutes to verify a prime using proth.exe, while the same verification on LLR would have been done in less than 2 minutes.

Oh! Okay!

Hey, thanks for the info. I did a little digging around and came up with some of that, but now everything is clear.

Thank you sirs!

You can perform a primality test on any k*b^n+-1 numbers with PFGW, which is built on George's FFT code and is much faster than Proth as well. Primality testing with PFGW is slower than PRP testing with LLR/PRP.