Wheel factorization: Efficient?

[10metreh]

BTW, 10462*1296^8192+1 is prime according to PFGW. No-one has said in this thread that they have proved it prime.

[retina]

Originally Posted by kar_bon

It's in the Top5000 here.

http://downforeveryoneorjustme.com/primes.utm.edu

[kar_bon]

Originally Posted by retina

http://downforeveryoneorjustme.com/primes.utm.edu

Yes, again. Yesterday and by now again not available for several hours!

[3.14159]

Yeah, the site went down for me as well. Also, the prime search has yielded nothing. Aaaaand, it'll continue. Sieved up to 415 billion, so there aren't any obvious composites around.

[science_man_88]

Originally Posted by 3.14159

Yeah, the site went down for me as well..

so seems this one lol http://primes.utm.edu/programs/NewPGen/

[3.14159]

Comics.I expect about 1-3 primes from this search.

[3.14159]

Since all practical ranges for the GFN up to 3 million are completed, and also for every exponent, I decided to search for primes that are a combination of Proths and GFNs (Not exactly, but a hybrid. Sorry if I'm sounding like a kook here, but, you'll probably get the idea.)

It's basically k * b^2[sup]n[/sup] + 1.

An example that I listed earlier on is 10462 * 1296⁸¹⁹² + 1, which has 25503 digits.

Since it *is* an arithmetic progression, I'm not shit out of luck for finding a larger example, since there are an infinite amount of primes in an arithmetic progression as well, although the odds do shrink away when larger examples are searched for. I'm processing 45910 candidates that were sieved for out of 1.1 million candidates originally. 1/24 of them were left, after about 2.5 to 3 hours' sieving on NewPGen. Each test takes 41 seconds.. 41 seconds * 45910 trials = 1882310 seconds, 86400 seconds = 1 day, so that makes ≈21.786 days if the search yields nothing. 1 in 30760 should be prime, 1.1 million/30760 leaves 35 primes expected in the search, and based on that, the first one should arrive in ≈14.4-15 hours. It's been at it for slightly less than 10.5 hours, so I expect one to arrive this afternoon, if not, tonight or the next day.

Expected prime: k * 77906⁸¹⁹² + 1. (40075 to 40080 digits)

Also: Is it easier to test when b = 2 * p, or when b = 2^a * p, where a > 1?

Update: I ran some tests, and I observed that divisibility by 2 had zero effect on the speed of the tests.

[CRGreathouse]

Originally Posted by 3.14159

1 in 30760 should be prime

How did you get that? I'm about to drop from exhaustion, so I may be missing something obvious, but I get 1 in (8192 log(77906) + 1)/2/38953*38952 =~ 46133, and this only increases (odds decrease) when I consider the k.

[3.14159]

Originally Posted by CRGreathouse

How did you get that? I'm about to drop from exhaustion, so I may be missing something obvious, but I get 1 in (8192 log(77906) + 1)/2/38953*38952 =~ 46133, and this only increases (odds decrease) when I consider the k.

Hmm.. I guess you had a somewhat long day. By the way, I already found a prime, so why speculate about odds?

[CRGreathouse]

Originally Posted by 3.14159

Hmm.. I guess you had a somewhat long day. By the way, I already found a prime, so why speculate about odds?

Why not?

[3.14159]

Originally Posted by CRGreathouse

Why not?

Well, if you insist, I used 1/(ln(x)-1). That gave me about 1 in 92282. Eliminating multiples of 2 and 3 gives 1 in 30760. But it's actually closer to 1 in 30761.