PARI's commands

[3.14159]

Originally Posted by CRGreathouse

I don't think this is GD, though; it's about math and programming primarily.

Yes, but the idea for a General Discussion forum should go in the Lounge/Soap Box. Or it should be a new forum section: Fuse the Lounge and Soap Box into General Discussion.

Mods, please move this into Forum Feedback.

[science_man_88]

I'm pointless to this forum.

[3.14159]

On finding k * n! + 1 primes:

I set the following params:

When n ≤ 200: Use APR-CL to prove it prime. (≈360-380 digits, max)*
When n > 200: Use 1-4 iterations of Miller-Rabin. (≈360-380+ digits)*

*Depends on the k-value used. Expect the numbers to increase if you use large k, and expect the probability to drop as well.**
** Can be made up for if factorial is fairly large (Ex: 1900!)

[CRGreathouse]

Seems broadly reasonable. What's the DLP bound on the chance of wrongly accepting a composite, assuming they act like random numbers?

[3.14159]

Originally Posted by CRGreathouse

Seems broadly reasonable. What's the DLP bound on the chance of wrongly accepting a composite, assuming they act like random numbers?

The odds of that are at worst 1 in 256.

[CRGreathouse]

Originally Posted by 3.14159

The odds of that are at worst 1 in 256.

Worst-case at the end of your spectrum, I take it you mean. I was asking about the average case, though.

[3.14159]

Also: I can't find any damn sieving implementations for specific files of k * n! + 1 (Multisieve only uses factorial primes and primorial primes, making it useless, NewPGen doesn't recognize k * n! + 1 unless I add an exponent to it. Quite frankly, k * (n!)^x + 1 is too slow.)

Looking for k * 2250! + 1. (18000 random k's, odds of finding a prime are 1 in 1k, with sieving that could have been improved to as much as.. 1 in 80.)

1 in 80 amongst 6575-digit primes is pretty good.

Solution: Use the trial division switch in PFGW.

[CRGreathouse]

I've posted the Pari bootcamp thread, as requested.

[CRGreathouse]

Originally Posted by 3.14159

Also: I can't find any damn sieving implementations for specific files of k * n! + 1

So write one. Loop over the primes from n+1 to as high as you like, and for each start at k = lift(Mod(-1,p)/n!) and use a step size of lift(Mod(1,p)/n!) to mark off candidates. (Check what I said in case of mistakes of finger or mind.)

[3.14159]

Originally Posted by CRGreathouse

So write one. Loop over the primes from n+1 to as high as you like, and for each start at k = lift(Mod(-1,p)/n!) and use a step size of lift(Mod(1,p)/n!) to mark off candidates. (Check what I said in case of mistakes of finger or mind.)

Nono, I have PFGW's trial division switch to help out. But, can you write a script anyway? Thank you.

Originally Posted by CRGreathouse

I've posted the Pari bootcamp thread, as requested.

I can't go to a private forum.

[CRGreathouse]

Originally Posted by 3.14159

Nono, I have PFGW's trial division switch to help out. But, can you write a script anyway? Thank you.

I just wrote half of it -- can you complete it?

Sieving is a lot more efficient than trial division.