mersenneforum.org Riesel Primes k*2^n-1, k<300 [Part II]
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2007-07-15, 20:54   #12
Cruelty

May 2005

2×809 Posts

Quote:
 Originally Posted by Kosmaj k=101.
My favourite - the next prime is @ n=9M

 2007-07-15, 21:02 #13 gd_barnes     May 2007 Kansas; USA 280216 Posts Status on k=289; gap closed 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
2007-07-15, 21:14   #14
gd_barnes

May 2007
Kansas; USA

2·32·569 Posts
Unusual gaps between primes

Quote:
 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

2007-07-15, 21:17   #15
gd_barnes

May 2007
Kansas; USA

1024210 Posts
k=101 question

Quote:
 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

2007-07-15, 21:17   #16
Flatlander
I quite division it

"Chris"
Feb 2005
England

31·67 Posts

Quote:
 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

2007-07-15, 22:43   #17
Cruelty

May 2005

2·809 Posts

Quote:
 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

Last fiddled with by Cruelty on 2007-07-15 at 22:46

 2007-07-16, 11:20 #18 Flatlander I quite division it     "Chris" Feb 2005 England 81D16 Posts k=55 tested to 800,000. Continuing.
 2007-07-16, 16:11 #19 amphoria     "Dave" Sep 2005 UK 2·19·73 Posts k=81 LLR at 840k. Continuing.
2007-07-16, 16:22   #20
gd_barnes

May 2007
Kansas; USA

2·32·569 Posts

Quote:
 Originally Posted by Cruelty You are correct, I have tested it 500000
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

2007-07-17, 08:16   #21
Cruelty

May 2005

31228 Posts

Quote:
 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

 2007-07-18, 03:00 #22 Kosmaj     Nov 2003 2·1,811 Posts k=105 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. Last fiddled with by Kosmaj on 2007-07-18 at 03:01

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