[QUOTE=axn]Sure. Just sieve till 1.17*10^17
[/QUOTE]

Actually, it's removed 1200 candidates today. It would only take 10 or 11 days to get the desired one in 20.

[QUOTE=3.14159;223728]I use Miller-Rabin for those proofs. And, the app divides by any odd number that ends in 1, 3, 7, or 9, regardless of whether or not it is prime.[/QUOTE]

...?

You asked about getting lists of small primes. bsquared asked "How small"? You said 10-30 digits. I explained that this would be too many primes, even if I took the square root interpretation. Now you say that you're not using trial division for numbers of that size.

Great... but then we're right back to bsquared's question: How big of a list do you want?

[QUOTE=3.14159;223743]Actually, it's removed 1200 candidates today. It would only take 10 or 11 days to get the desired one in 20.[/QUOTE]

Wow. You can sieve till 10^17 in 10 days! That means you must have 10000 cores sieving!!!

[QUOTE=3.14159;223743]Actually, it's removed 1200 candidates today. It would only take 10 or 11 days to get the desired one in 20.[/QUOTE]

Various projected milestones
[CODE]p=6.34e12: 1 in 15
p=4.52e13: 1 in 16
p=3.23e14: 1 in 17
p=2.30e15: 1 in 18
p=1.64e16: 1 in 19
p=1.17e17: 1 in 20[/CODE]

PS:- These numbers are specific for your current sieve.

[QUOTE=CRGreathouse]You asked about getting lists of small primes. bsquared asked "How small"? You said 10-30 digits. I explained that this would be too many primes, even if I took the square root interpretation. Now you say that you're not using trial division for numbers of that size.
[/QUOTE]


Okay: To clear things up:
1. 10 digits would only require division up to at most 316227.
2. Trial division - Up to about 18 digits.
3. Miller-Rabin - Up to about 30 digits.

Everything is cleared.

[QUOTE=axn]Wow. You can sieve till 10^17 in 10 days! That means you must have 10000 cores sieving!!![/QUOTE]

HAHAHA, the most entertaining strawman I've ever heard.

[QUOTE=axn]PS:- These numbers are specific for your current sieve.[/QUOTE]

For my specific case? :orly owl:

[QUOTE=3.14159;223778]Okay: To clear things up:
1. 10 digits would only require division up to at most 316227.
2. Trial division - Up to about 18 digits.
3. Miller-Rabin - Up to about 30 digits.

Everything is cleared.[/QUOTE]

So you're asking about making a list of primes up to 10^9?

I just use Pari for that size; its algorithm is plenty good enough for me.
[code]default(primelimit,10^9)[/code]
takes about 3.3 seconds on my machine.

You can also try Bernstein's primegen if you like.

[QUOTE=CRGreathouse;223783]So you're asking about making a list of primes up to 10^9?

I just use Pari for that size; its algorithm is plenty good enough for me.
[code]default(primelimit,10^9)[/code]
takes about 3.3 seconds on my machine.

You can also try Bernstein's primegen if you like.[/QUOTE]


think he's asking for 10^10 to 10^30 myself but I could be wrong.

though depending base it could be up to infinity base 2 about 10^9 base 10 10^10-9.99999999999999999999999999999*10^30 base 16 16^10-F.FFFFFFFFFFFFFFFFFFFFFFFFFFFFF16^30 ?

[QUOTE=science_man_88]think he's asking for 10^10 to 10^30 myself but I could be wrong.
[/QUOTE]

Trial division proofs only require that you divide up to the [B]square root[/B] of that number. Only primes up to 10[sup]9[/sup] are needed to prove the primality of any 18-digit number. And about 10-30 iterations of Miller-Rabin (random-based) will guarantee the primality of any number up to 10[sup]30[/sup].

[QUOTE=3.14159;223820]Trial division proofs only require that you divide up to the [B]square root[/B] of that number. Only primes up to 10^9 are needed to prove the primality of any 18-digit number.[/QUOTE]

I was talking of the range you wanted to prove I wasn't aware about what he was talking about obviously. I know about the sqrt part.

I tested the (ispseudoprime) function to the comparison against my methods, coded.

The results are: (For a 5628-digit PRP):
ispseudoprime: 36.083 seconds
isSPRP: 12.355 seconds

Nearly three times as fast.

[QUOTE=3.14159;223820]And about 10-30 iterations of Miller-Rabin (random-based) will guarantee the primality of any number up to 10[sup]30[/sup].[/QUOTE]

For some meaning of "guarantee", at least.

Of course as I've said, if you're looking to get that kind of certainty you'd be better off with one Miller-Rabin and a few applications of some modern test, e.g. Damgård-Frandsen; for the time it would take you to do 10 M-Rs (1 M-
R + 3 D-F), you can get higher confidence than you'd get for 30 M-Rs: 1/142657607172096 vs. only 1/1073741824. They're better in the average case, too.

[QUOTE=3.14159;223822]I tested the (ispseudoprime) function to the comparison against my methods, coded.

The results are: (For a 5628-digit PRP):
ispseudoprime: 36.083 seconds
isSPRP: 12.355 seconds

Nearly three times as fast.[/QUOTE]

Sure, because ispseudoprime() is stronger. If you want just one test do
[code]ispseudoprime(n, 1)[/code]
(though that will still do some trial division).