PARI's commands

[CRGreathouse]

Originally Posted by 3.14159

That code is pretty long. Are you sure you had no simpler way of writing it?

On the contrary, I could have written it to be one-third the size if I had time.

[3.14159]

Originally Posted by CRGreathouse

On the contrary, I could have written it to be one-third the size if I had time.

Excellent.

[3.14159]

It's rare that sm88 doesn't have much to contribute today.

[science_man_88]

Originally Posted by 3.14159

It's rare that sm88 doesn't have much to contribute today.

yeah well between guest research on my mom's cancer type and family history plus playing with CRG's substring code to check for his requirements it's hard the only thing i know about the code is glue isn't defined in Pari last I checked (and i did check)

[3.14159]

Originally Posted by science_man_88

yeah well between guest research on my mom's cancer type and family history plus playing with CRG's substring code to check for his requirements it's hard the only thing i know about the code is glue isn't defined in Pari last I checked (and i did check)

I've recently been messing with vk, to test the sieve's efficiency using factor-rich vs. prime numbers.

Prime numbers tend to have the most candidates eliminated. Using the primorials, however, I think the sieve met its match.

Ex: I defined the primorial function as p(n), where n is the nth prime.

Trying p(90), I don't think even 1/2 of the candidates would be eliminated if I were to sieve to 10⁹

[science_man_88]

Originally Posted by 3.14159

I've recently been messing with vk, to test the sieve's efficiency using factor-rich vs. prime numbers.

Prime numbers tend to have the most candidates eliminated. Using the primorials, however, I think the sieve met its match.

Ex: I defined the primorial function as p(n), where n is the nth prime.

Trying p(90), I don't think even 1/2 of the candidates would be eliminated if I were to sieve to 10⁹

the definition only works if you have a high enough prime limit in one sense if you use the function prime(x) if it's greater than primelimit you'd have to adapt it a bit.

[CRGreathouse]

Originally Posted by science_man_88

the only thing i know about the code is glue isn't defined in Pari last I checked (and i did check)

I defined it in post #901.

[CRGreathouse]

Originally Posted by 3.14159

I've recently been messing with vk, to test the sieve's efficiency using factor-rich vs. prime numbers.

Prime numbers tend to have the most candidates eliminated. Using the primorials, however, I think the sieve met its match.

Primorial bases will have more candidates than prime bases, but if you sieve to any reasonable level candidates from either will produce primes at the same rate at a given size.

Originally Posted by 3.14159

Ex: I defined the primorial function as p(n), where n is the nth prime.

Trying p(90), I don't think even 1/2 of the candidates would be eliminated if I were to sieve to 10⁹

I would have expected 77% of the candidates to be removed at that level, using Mertens' Theorem (and direct calculation with the first 24 primes).

[3.14159]

Originally Posted by CRGreathouse

Primorial bases will have more candidates than prime bases, but if you sieve to any reasonable level candidates from either will produce primes at the same rate at a given size.

It depends on one's definition of "reasonable". Some would say reasonable is 10⁶, others would say it's 10¹⁵.

Originally Posted by CRGreathouse

I would have expected 77% of the candidates to be removed at that level, using Mertens' Theorem (and direct calculation with the first 24 primes).

Only way to find out is to try it for yourself. Give NewPGen a few seconds for a certain k-range for k * p(90) + 1. Or give vk a few minutes to come up with all the candidates.

I'm going to search for k * 1621!² + 1, where k is between 10500 and 80500. The amount of digits should be about.. 9008-9010. (9008 = 2⁴ * 563).

[3.14159]

Well, I sieved to 700M. Apparently, there are still a load of candidates left.

[CRGreathouse]

Originally Posted by 3.14159

It depends on one's definition of "reasonable". Some would say reasonable is 10⁶, others would say it's 10¹⁵.

I grant that there are people who would consider either reasonable. My statement holds for both definitions, and indeed a wider range on both sides.

Originally Posted by 3.14159

Only way to find out is to try it for yourself. Give NewPGen a few seconds for a certain k-range for k * p(90) + 1. Or give vk a few minutes to come up with all the candidates.

If you're interested, go ahead. I'd rather spend the time looking up better estimates of the product (with or without the assumption of the RH).