mersenneforum.org  

Go Back   mersenneforum.org > Prime Search Projects > Riesel Prime Search

Reply
 
Thread Tools
Old 2007-07-15, 20:54   #12
Cruelty
 
Cruelty's Avatar
 
May 2005

2·809 Posts
Default

Quote:
Originally Posted by Kosmaj View Post
k=101.
My favourite - the next prime is @ n=9M
Cruelty is offline   Reply With Quote
Old 2007-07-15, 21:02   #13
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

3·11·307 Posts
Default 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
gd_barnes is offline   Reply With Quote
Old 2007-07-15, 21:14   #14
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

3·11·307 Posts
Default Unusual gaps between primes

Quote:
Originally Posted by Kosmaj View Post
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 is offline   Reply With Quote
Old 2007-07-15, 21:17   #15
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

3·11·307 Posts
Default k=101 question

Quote:
Originally Posted by Cruelty View Post
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
gd_barnes is offline   Reply With Quote
Old 2007-07-15, 21:17   #16
Flatlander
I quite division it
 
Flatlander's Avatar
 
"Chris"
Feb 2005
England

31×67 Posts
Default

Quote:
Originally Posted by Kosmaj View Post
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
Flatlander is offline   Reply With Quote
Old 2007-07-15, 22:43   #17
Cruelty
 
Cruelty's Avatar
 
May 2005

2·809 Posts
Default

Quote:
Originally Posted by gd_barnes View Post
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
Cruelty is offline   Reply With Quote
Old 2007-07-16, 11:20   #18
Flatlander
I quite division it
 
Flatlander's Avatar
 
"Chris"
Feb 2005
England

31×67 Posts
Default

k=55 tested to 800,000. Continuing.
Flatlander is offline   Reply With Quote
Old 2007-07-16, 16:11   #19
amphoria
 
amphoria's Avatar
 
"Dave"
Sep 2005
UK

2·19·73 Posts
Default k=81

LLR at 840k. Continuing.
amphoria is offline   Reply With Quote
Old 2007-07-16, 16:22   #20
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

1013110 Posts
Default

Quote:
Originally Posted by Cruelty View Post
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
gd_barnes is offline   Reply With Quote
Old 2007-07-17, 08:16   #21
Cruelty
 
Cruelty's Avatar
 
May 2005

110010100102 Posts
Default

Quote:
Originally Posted by gd_barnes View Post
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
Cruelty is offline   Reply With Quote
Old 2007-07-18, 03:00   #22
Kosmaj
 
Kosmaj's Avatar
 
Nov 2003

2×1,811 Posts
Default 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
Kosmaj is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Riesel base 3 reservations/statuses/primes KEP Conjectures 'R Us 1038 2020-05-24 09:22
Proth and Riesel Primes lukerichards Number Theory Discussion Group 7 2018-01-20 16:47
Riesel primes Primeinator Information & Answers 12 2009-07-19 23:30
Sierpinski/Riesel Base 5: Post Primes Here robert44444uk Sierpinski/Riesel Base 5 358 2008-12-08 16:28
Riesel.15k.org LLRnet Primes Found! SlashDude 15k Search 3 2004-06-14 16:07

All times are UTC. The time now is 00:25.

Sat Jun 6 00:25:19 UTC 2020 up 72 days, 21:58, 0 users, load averages: 1.52, 1.28, 1.21

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.