mersenneforum.org  

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

Reply
 
Thread Tools
Old 2007-04-13, 04:13   #12
robert44444uk
 
robert44444uk's Avatar
 
Jun 2003
Oxford, UK

1,901 Posts
Default E58 Payam monsters

Some very high weight k from E58 payams:

32579969380008913005 8525 8521 (52 primes up to n=4000)
107251588234045704735 8406 8427 (51)
13807832114791617045 8422 8426 (55)
61105047309618807495 8435 8425 (59)
103580176519428233625 8419 8417 (59)
23414125704058421475 8406 8398
88808249896288517595 8396 8397
84315984863907089865 8387 8391
14785001407354998105 8402 8389
127417329985126803765 8388 8389
76394646230550311235 8390 8388
60906262455634018995 8384 8383
69653119293945259215 8383 8381
32553911156616844995 8371 8369
37287243950233762485 8356 8368
140901287463148857645 8362 8363
8510826865344068265 8367 8358
84981504576267664365 8356 8358
39007792020021273735 8358 8351
41461979133931229445 8366 8349
132699500417439184515 8345 8348
29875821764528915175 8331 8345
99215945779882385025 8342 8345
103449671808231170565 8342 8344
34392540738877805055 8337 8342
130261440899098442505 8360 8342
80147906108029855095 8335 8337
30351653111902964985 8335 8336
122887606923246617595 8335 8336
69489454966333401285 8344 8334
7386718138834077615 8329 8331
61665332067869044515 8334 8329
119444814610232214675 8327 8329
50246977722089253105 8340 8328
117259940292110939895 8325 8328

Again these are not necessarily rich in primes, that is all down to chance in the early n. None of the top 5 were rich in primes in the first 100 n.
robert44444uk is offline   Reply With Quote
Old 2007-06-19, 23:39   #13
roger
 
roger's Avatar
 
Oct 2006

4048 Posts
Default

Where can I find this program that Axn1 produced?

The way I have found (some) k's is NewPGens Cunningham chain sieve.

Thanks,

Roger
roger is offline   Reply With Quote
Old 2007-06-20, 01:18   #14
Kosmaj
 
Kosmaj's Avatar
 
Nov 2003

2·1,811 Posts
Default

Attached to post #9, a few posts up.

Quote:
Where can I find this program that Axn1 produced?
Kosmaj is offline   Reply With Quote
Old 2007-12-16, 05:11   #15
roger
 
roger's Avatar
 
Oct 2006

22·5·13 Posts
Default

How are the nash weights calculated? Also, I've read above and elsewhere in mersenneforum that the higher the nash weight (like 8000+ as in the above posts), the better the chances of the k. However, I just found a reasonably good one with so far 112 by n=16332, and the weight is "3641 3652" In case it matters, it is a ep130 generated by payamx.

Thanks!

roger

Last fiddled with by roger on 2007-12-16 at 05:14
roger is offline   Reply With Quote
Old 2007-12-16, 08:13   #16
VBCurtis
 
VBCurtis's Avatar
 
"Curtis"
Feb 2005
Riverside, CA

11·401 Posts
Default

Nash weight is simply the number of candidates left after sieving to some arbitrary value (I think 512). The two numbers are from sieving the 0-10k range and the 100-110k range.

Sieving to 1 million or some similar higher p would produce a better gauge of candidate density, but Nash is long established. The best "known" predictor of prime density is candidate density- as far as we know, the chance a number has of being prime is a function of sieve depth, size of number, but not the actual k-value. Some believe we will find other factors with more data, certain k's or types of k's more or less likely to produce primes than others, but nothing is yet known. I suppose one hope is a statistical analysis of large pools of data once we have such a pool; even then, determining causation is a long way from discovering patterns or potential patterns.
-Curtis
VBCurtis is online now   Reply With Quote
Old 2007-12-16, 08:22   #17
kar_bon
 
kar_bon's Avatar
 
Mar 2006
Germany

54428 Posts
Default

to calculate the nash weights look here: http://www.mersenneforum.org/showthread.php?t=7213.
higher nash is equal higher chance of finding is quite correct: the nash weight indicates how many candidates are remain after a sieve limit and therefore the more candidates the more primes are possible. it's only a point of reference not a guarantee!
on the other side: the more candidates the more prime tests you have to do so it's very time consuming to go up in higher ranges of n!
your k with nash 3641 and 112 primes you can see that the nash is only a value without a predictable number of primes of a k!

(2nd info for rogers post, some minutes after )

Last fiddled with by kar_bon on 2007-12-16 at 08:24
kar_bon is offline   Reply With Quote
Old 2007-12-16, 22:17   #18
roger
 
roger's Avatar
 
Oct 2006

22×5×13 Posts
Default

Thanks VBCurtis and kar_bon, it makes more sense now!

Regarding payam numbers, is there a website that details what e values have been searched, and to what level?

I'm currently doing a search with ep130 (because I know the Riesel forum is for k*2^n-1), have sieved for numbers to 1T, and tested them to 250B. So far I've had two k's give 99 primes by n=10,000, but none at the critical 100 mark

Curtis, when you said 'candidate density' did you mean the average gap between primes up to a certain level (eg gap=100 by n=10,000 = 100 primes or gap=200 by n=10,000 = 50 primes)? Or the amount of primes below a certain value?

Thanks!

roger
roger is offline   Reply With Quote
Old 2007-12-17, 00:24   #19
kar_bon
 
kar_bon's Avatar
 
Mar 2006
Germany

2×3×52×19 Posts
Default

the page from robert is here http://home2.btconnect.com/rwsmith/pp/payam1.htm but it's from 2002.
so the best info you can get from robert himself. see post #1 here.
kar_bon is offline   Reply With Quote
Old 2007-12-17, 01:46   #20
axn
 
axn's Avatar
 
Jun 2003

4,721 Posts
Default

He has an updated site at http://robert.smith44444.googlepages...umberresources
axn is offline   Reply With Quote
Old 2007-12-18, 01:11   #21
VBCurtis
 
VBCurtis's Avatar
 
"Curtis"
Feb 2005
Riverside, CA

441110 Posts
Default

Quote:
Originally Posted by roger View Post
Thanks VBCurtis and kar_bon, it makes more sense now!

Curtis, when you said 'candidate density' did you mean the average gap between primes up to a certain level (eg gap=100 by n=10,000 = 100 primes or gap=200 by n=10,000 = 50 primes)? Or the amount of primes below a certain value?

Thanks!

roger
By candidate density, I mean the number of candidates left to LLR after a sieve. The fraction of candidates that are prime is known only to depend on n and sieve depth, but clearly this is not the case uniformly; one way to look at it is to imagine a set of k's, each with 6000 candidates per 10,000 to test after sieving to 1M. If you run each of these k's through LLR to 50k, they might average 80 primes each. However, they will not *all* have 80 primes- the list might go 72,75,88,97,65,83.
You can think of the number of primes as a random variable, and look at its mean and variance, etc. Or, you can hope that past performance is a prediction of future prime density, and hope k's with high numbers of primes for their weight will continue to have higher-than-predicted numbers of primes going forward.

Some searchers hope someday to have so much data that we can show this distribution is more than just noise- that some k's really are more likely (or less) to produce primes.
-Curtis
VBCurtis is online now   Reply With Quote
Old 2007-12-18, 18:37   #22
roger
 
roger's Avatar
 
Oct 2006

22·5·13 Posts
Default

Quote:
you can hope that past performance is a prediction of future prime density, and hope k's with high numbers of primes for their weight will continue to have higher-than-predicted numbers of primes going forward.
I've been doing this for my searches, using the average increase across a large amount of primes, and it usually comes out pretty close.

Quote:
Some searchers hope someday to have so much data that we can show this distribution is more than just noise- that some k's really are more likely (or less) to produce primes.
This is where the Payam numbers came from, right? By looking at the factors of a series, to learn which k's have certain factors, and eliminating them from the list of especially good k's?

Thanks!

roger
roger is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
RPS 7th Drive: 21 High-Weight Ks Kosmaj Riesel Prime Search 543 2020-04-25 02:35
RPS 9th Drive: Yet Another Bunch of High-Weight Ks Kosmaj Riesel Prime Search 456 2018-06-23 20:31
RPS 12th Drive: 13 high weight Ks from the 2000-2300 interval Thomas11 Riesel Prime Search 59 2015-04-20 14:05
High weight k's kar_bon Riesel Prime Data Collecting (k*2^n-1) 26 2013-09-11 23:12
Very high-weight k's - co-ordinating a search for top5k primes f1pokerspeed Riesel Prime Search 4 2012-08-07 07:30

All times are UTC. The time now is 20:49.

Fri Oct 30 20:49:52 UTC 2020 up 50 days, 18 hrs, 1 user, load averages: 1.67, 1.90, 1.88

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.