[QUOTE=3.14159;227146]That code is pretty long. Are you sure you had no simpler way of writing it? :no:[/QUOTE]

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

[QUOTE=CRGreathouse]On the contrary, I could have written it to be one-third the size if I had time.
[/QUOTE]

Excellent.

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

[QUOTE=3.14159;227179]It's rare that sm88 doesn't have much to contribute today.[/QUOTE]

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)

[QUOTE=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)
[/QUOTE]

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 10[sup]9[/sup]

[QUOTE=3.14159;227183]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 10[sup]9[/sup][/QUOTE]

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.

[QUOTE=science_man_88;227182]the only thing i know about the code is glue isn't defined in Pari last I checked (and i did check)[/QUOTE]

I defined it in post #901.

[QUOTE=3.14159;227183]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.[/QUOTE]

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.

[QUOTE=3.14159;227183]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 10[sup]9[/sup][/QUOTE]

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).

[QUOTE=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.
[/QUOTE]

It depends on one's definition of "reasonable". Some would say reasonable is 10[sup]6[/sup], others would say it's 10[sup]15[/sup].


[QUOTE=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).
[/QUOTE]

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![sup]2[/sup] + 1, where k is between 10500 and 80500. The amount of digits should be about.. 9008-9010. (9008 = 2[sup]4[/sup] * 563).

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

[QUOTE=3.14159;227194]It depends on one's definition of "reasonable". Some would say reasonable is 10[sup]6[/sup], others would say it's 10[sup]15[/sup].[/QUOTE]

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.

[QUOTE=3.14159;227194]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.[/QUOTE]

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).