Thread for posting tiny primes - Page 51

CRGreathouse · 2010-09-20, 05:12

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).

3.14159 · 2010-09-20, 21:54

Code:

17:50:25 35949 k's remaining. p=27996694779059 divides k=1397385

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.

CRGreathouse · 2010-09-20, 23:17

Quote:

Originally Posted by 3.14159

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.

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.)

kar_bon · 2010-09-20, 23:27

Quote:

Originally Posted by CRGreathouse

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.)

Probably, no guarantee!

3.14159 · 2010-09-21, 00:06

All primes in the range? I'm content enough with one 179k-digit prime.

3.14159 · 2010-09-21, 00:10

Quote:

Originally Posted by Karsten

Probably, no guarantee!

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.)

firejuggler · 2010-09-21, 00:26

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

CRGreathouse · 2010-09-21, 00:54

Quote:

Originally Posted by kar_bon

Probably, no guarantee!

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:

Originally Posted by 3.14159

All primes in the range? I'm content enough with one 179k-digit prime.

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%.

3.14159 · 2010-09-21, 01:11

Quote:

Originally Posted by 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%.

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:

Originally Posted by NewPGen

21:09:07 35891 k's remaining. p=29574929898821 divides k=1944541

CRGreathouse · 2010-09-21, 01:19

Quote:

Originally Posted by 3.14159

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

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

3.14159 · 2010-09-21, 01:21

Quote:

Originally Posted by Charles

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

I made the false assumption of looking at all the candidates.

2010-09-20, 21:54	#552
3.14159 May 2010 Prime hunting commission. 3220₈ Posts	Code: 17:50:25 35949 k's remaining. p=27996694779059 divides k=1397385 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. Last fiddled with by 3.14159 on 2010-09-20 at 21:54

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2010-09-20, 05:12	#551
CRGreathouse Aug 2006 3·1,993 Posts	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).

2010-09-21, 00:06	#555
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	All primes in the range? I'm content enough with one 179k-digit prime.

2010-09-21, 00:26	#557
firejuggler Apr 2010 Over the rainbow 101000101110₂ Posts	so you are 'bound' to find about 7 primes? I know odds don't add