PARI's commands

[science_man_88]

for(n=1,10,for(k=1,20,if(isprime(k*n!+1),print(k","n))))

is what I did.

[3.14159]

Originally Posted by CRGreathouse

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

Sieving is a lot more efficient than trial division.

Show me the script. That will answer the question:

Also: How is sieving not wide-range trial-division?

[CRGreathouse]

Originally Posted by 3.14159

Show me the script.

I didn't write it, and don't intend on writing it.

Originally Posted by 3.14159

How is sieving not wide-range trial-division?

I've tried to explain this to you twice, and I failed both times. I guess I'm not that good of a teacher.

[3.14159]

Originally Posted by CRGreathouse

I've tried to explain this to you twice, and I failed both times. I guess I'm not that good of a teacher.

Nevermind, I get it now.

1. Establish the first number larger than p such that n%p = 0. (Ex: 311, 622%311 = 0.)
2. Count by p and cross off.

That it?

[CRGreathouse]

Originally Posted by science_man_88

for(n=1,10,for(k=1,20,if(isprime(k*n!+1),print(k","n))))

is what I did.

Yes. The intent is to avoid as many isprime() calls as possible, though. When you're working with numbers that take a long time to test you don't want to run extra checks.

I wrote a quick siever today for a problem I'm working on, and it managed to remove about 200,000 candidates, saving what would have otherwise been a few months of work.

[CRGreathouse]

Originally Posted by 3.14159

Nevermind, I get it now.

1. Establish the first number larger than p such that n%p = 0. (Ex: 311, 622%311 = 0.)
2. Count by p and cross off.

Yes, that's the basic idea. #2 has to be modified when you're working with numbers that aren't consecutive, like k * n! + 1 or k * 2^n + 1. I gave the relevant calculations (hopefully correct!) above.

[3.14159]

Originally Posted by CRGreathouse

Yes, that's the basic idea. #2 has to be modified when you're working with numbers that aren't consecutive, like k * n! + 1 or k * 2^n + 1. I gave the relevant calculations (hopefully correct!) above.

You mean, these?:

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.)

Originally Posted by CRGreathouse

I didn't write it, and don't intend on writing it.

How in the world did you manage to contradict yourself so vividly?
This, to me, is a glaring red flag.

[CRGreathouse]

Originally Posted by 3.14159

How in the world did you manage to contradict yourself so vividly?

I see no contradiction.

[science_man_88]

Originally Posted by CRGreathouse

I see no contradiction.

how is telling you to write something Pi a contradiction of I didn't write one I don't plan on such a thing. it's not.

[3.14159]

Originally Posted by science_man_88

how is telling you to write something Pi a contradiction of I didn't write one I don't plan on such a thing. it's not.

Doesn't "I wrote 1/2 of the script", and "I did not write it, nor do I intend to write it", sound a bit like 1 = 2 to you?

P.S: 816280180 * 2250! + 1 is prime. (≈6575 digits)

[CRGreathouse]

Originally Posted by 3.14159

Doesn't "I wrote 1/2 of the script", and "I did not write it, nor do I intend to write it", sound a bit like 1 = 2 to you?

No. I wrote the key calculations for the script, in the scripting language. I did not write the script that would contain those calculations. (If it's not worth your time to do it, why would it be worth mine?)