Riesel Primes k*2^n-1, k<300 [Part II]

[Cruelty]

Originally Posted by Kosmaj

k=101.

My favourite - the next prime is @ n=9M

[gd_barnes]

I have now 'officially' closed the gap on k=289. I've now tested all the way from n=260K up past the next known prime at n=501991. I found that one prime that Bo had already found.

I'm actually testing all the way to n=520K to verify some prior results and LLR is currently at n=503K.


Gary

[gd_barnes]

Originally Posted by Kosmaj

No, I think it's proven that if k has a prime for one n, then there are primes for infinitely many. But the gaps between primes can be large. See for example k=253 and k=101.

Good question by Flatlander. I think the term 'large' in describing the gaps between primes is a 'large' understatement. They can be flat-out enourmous!

I'll throw out a somewhat similiar situation in my gap-filling efforts...
Although it has many primes, k=289 is an excellent example of one of the more extreme gaps between primes that I've seen for a k that we would not consider low-weight. It has primes at 55693, 60243, 67891, 77391, 90201, then a 'monster' gap of no primes (now confirmed by me), followed by primes at 501991, 509401, 610737, 728205. This, I think, is far more unusual than a low-weight k having a gap between primes of more than 1M.

Go figure. I think an entire thread could be dedicated to record gaps between primes for different weights of k. These unpredictible gaps are what makes primes so fun!


Gary

[gd_barnes]

Originally Posted by Cruelty

My favourite - the next prime is @ n=9M

Hasn't that one only been tested to n=1M with its largest prime at n=900358? Just curious if I have missed something somewhere.

But that is a huge gap between n=94194 and 900358!


Gary

[Flatlander]

Originally Posted by Kosmaj

No, I think it's proven that if k has a prime for one n, then there are primes for infinitely many. But the gaps between primes can be large. See for example k=253 and k=101.

But not proven for k=1?
http://en.wikipedia.org/wiki/Mersenne_prime

[Cruelty]

Originally Posted by gd_barnes

Hasn't that one only been tested to n=1M with its largest prime at n=900358? Just curious if I have missed something somewhere.

You are correct, I have tested it 500000<n<1000000 so far. Shortly I will begin testing it in the 1M<n<2M range. When I have announced prime @ n=900358, Kosmaj suggested that the next one might be @ n~9M because last 3 "n"s for this k that start with "9" were primes

[Flatlander]

k=55 tested to 800,000. Continuing.

[amphoria]

LLR at 840k. Continuing.

[gd_barnes]

Originally Posted by Cruelty

You are correct, I have tested it 500000<n<1000000 so far. Shortly I will begin testing it in the 1M<n<2M range. When I have announced prime @ n=900358, Kosmaj suggested that the next one might be @ n~9M because last 3 "n"s for this k that start with "9" were primes

Ah, I get it now.

Well...you should test k=101 from n=9M to 10M!! That'd be funny if you found one pretty quick. Of course it would take ages to process each candidate!


Gary

[Cruelty]

Originally Posted by gd_barnes

Well...you should test k=101 from n=9M to 10M!! That'd be funny if you found one pretty quick. Of course it would take ages to process each candidate!

Actually it takes ~2 days on 3GHz C2D

[Kosmaj]

Cruelty, but that's great news, that you are already working on them!

BTW, Flatlander stopped n=105 at n=541300 and kindly sent me the rest of his file sieved to 4.2T. If anybody is interested in continuing tests, just let me know. Otherwise I'll send the block to about 570k to B'maxx. If there is enough interest I can open a thread for group testing as well.