It would be nice to have a script that does these sorts of calculations automatically: find settings that minimize various things, and then estimates of how long to find the first prime, how long to finish the range, etc. under different settings (with at least the first showing maybe the 5%, 25%, 50%, 75%, and 95% probability timings).

[code]17:50:25 35949 k's remaining. p=27996694779059 divides k=1397385[/code]

This is excellent. I am at under 36000 k's. Very excellent indeed. It would probably take 4-8 times that effort to reach under 35000 k's.

[QUOTE=3.14159;230650]This is excellent. I am at under 36000 k's. Very excellent indeed. It would probably take 4-8 times that effort to reach under 35000 k's.[/QUOTE]

Well, if you take my advice you should sieve until roughly 35200 remain; if you take mdettweiler's advice, sieve until roughly 34300 remain.

His advice is appropriate if you intend to find all primes in the range; mine if you intend to find only the first. (My advice gets you to the first faster but the second slower.)

[QUOTE=CRGreathouse;230668]His advice is appropriate if you intend to find all primes in the range; mine if you intend to find only the first. (My advice gets you to the first faster but the second slower.)[/QUOTE]

Probably, no guarantee! :smile:

All primes in the range? I'm content enough with [B]one[/B] 179k-digit prime. :smile:

[QUOTE=Karsten;230672]Probably, no guarantee! :smile:[/QUOTE]

And we shall leave that, to the odds..

Which are about.. 1 in 7400 at worst, and, if counting out 3 as a factor is valid (All primes greater than 3 = 6n+1 or 6n-1); 1 in 4935 at best! (That is, at the moment.)

so you are 'bound' to find about 7 primes? I know odds don't add

[QUOTE=kar_bon;230672]Probably, no guarantee! :smile:[/QUOTE]

Yes, of course. And I haven't even proven that my method is optimal under the random model -- in fact it's probably slightly suboptimal. But it's a reasonable first estimate.

[QUOTE=3.14159;230677]All primes in the range? I'm content enough with [B]one[/B] 179k-digit prime. :smile:[/QUOTE]

In this case the range won't contain many primes, maybe 2-6. The probability that you'll find at least one prime is something like 99%.

[QUOTE=Charles]In this case the range won't contain many primes, maybe 2-6. The probability that you'll find at least one prime is something like 99%.
[/QUOTE]

I looked at a range of 2 million; I need to check the database to ensure I am not going to discover any previously found primes.

... Found no previously submitted prime in that range. I'm lucky others only search small k-values.

Based on those odds; I should on average find at least 10 primes. Or am I making the gambler's fallacy?

[QUOTE=NewPGen]21:09:07 35891 k's remaining. p=29574929898821 divides k=1944541[/QUOTE]

[QUOTE=3.14159;230699]Based on those odds; I should on average find at least 10 primes. Or am I making the gambler's fallacy?[/QUOTE]

By my calculations your odds of finding 10 or more primes in this range is approximately 2.5%.

[QUOTE=Charles]By my calculations your odds of finding 10 or more primes in this range is approximately 2.5%.
[/QUOTE]

I made the false assumption of looking at all the candidates. :no: