mersenneforum.org  

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

Reply
 
Thread Tools
Old 2021-10-22, 15:57   #287
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

2·4,787 Posts
Default

Quote:
Originally Posted by pepi37 View Post
If I may ask how many candidates remain after that ?
Sure.
Attached Thumbnails
Click image for larger version

Name:	K_w.png
Views:	32
Size:	11.6 KB
ID:	26004  
Batalov is offline   Reply With Quote
Old 2021-10-22, 17:44   #288
bur
 
bur's Avatar
 
Aug 2020
79*6581e-4;3*2539e-3

13·31 Posts
Default New Primorial Prime found

Recently a new -1 type primorial prime was found at PRPNet.

3267113# - 1

It has 1418398 digits, making it the largest known one. The last -1 primorial prime was found more than 9 years ago, so this is quite the finding. The last +1 primorial prime hit is from 2001 btw. 20 years ago. :D

I think it's an interesting type of prime due to its involvement in Euclid's proof of the infinitude of primes. Not many people seem to hunt for them though and they seem somewhat scarce taking into account that N+-1 has lots of factors.

MODERATOR NOTE: Moved to this thread, which already has this post and several followups related to this number.

Last fiddled with by Dr Sardonicus on 2021-10-23 at 02:37
bur is offline   Reply With Quote
Old 2021-10-22, 18:03   #289
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

387610 Posts
Default

Quote:
Originally Posted by bur View Post
Recently a new -1 type primorial prime was found at PRPNet.

3267113# - 1

It has 1418398 digits, making it the largest known one. The last -1 primorial prime was found more than 9 years ago, so this is quite the finding. The last +1 primorial prime hit is from 2001 btw. 20 years ago. :D

I think it's an interesting type of prime due to its involvement in Euclid's proof of the infinitude of primes. Not many people seem to hunt for them though and they seem somewhat scarce taking into account that N+-1 has lots of factors.
PRP tests for these are quite quick, compared to proofs. However they need generic modular reduction for Fermat PRP tests, whereas small-k Riesel and Proth prime run 4x (?) faster using a special mod.

The rarity of these numbers might put the next beyond the powers of Batalov-Propper.

MODERATOR NOTE: Moved to this thread, which already has this post and several followups related to this number.

Last fiddled with by Dr Sardonicus on 2021-10-23 at 02:38
paulunderwood is offline   Reply With Quote
Old 2021-10-25, 17:34   #290
bur
 
bur's Avatar
 
Aug 2020
79*6581e-4;3*2539e-3

13×31 Posts
Default

Thanks for moving the post.
Quote:
The rarity of these numbers might put the next beyond the powers of Batalov-Propper.
Who knows, it's not like where GIMPS is currently at where 20M+ consecutive candidates are composite - at least I don't think so.



I always forget the estimate for the digit size of primorials but the FFT size remains very managable even up to 20,000,000# where it's 3M.


So if anyone was willing to put some larger ressources towards primorials or factorials, I'm pretty sure it'll yield some nice results before ending up in GIMPS waters.
bur is offline   Reply With Quote
Old 2021-10-25, 20:53   #291
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

32·557 Posts
Default

Quote:
Originally Posted by bur View Post
I always forget the estimate for the digit size of primorials but the FFT size remains very managable even up to 20,000,000# where it's 3M.
The number of decimal digits in pk is roughly pk/ln(10). We have

? 3267113/log(10)
%1 = 1418889.1476543787883927627556683863802

As indicated above, 3267113# - 1 actually has 1418398 digits.

The estimate is a consequence of the Prime Number Theorem, which gives the asymptotic estimate

ln(pk#) = ln(2) + ln(3) + ... + ln(pk) ~ pk
Dr Sardonicus is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Patterns in primes that are primitive roots / Gaps in full-reptend primes mart_r Prime Gap Searches 14 2020-06-30 12:42
Mersenne Primes p which are in a set of twin primes is finite? carpetpool Miscellaneous Math 3 2017-08-10 13:47
Distribution of Mersenne primes before and after couples of primes found emily Math 34 2017-07-16 18:44
Conjecture about Mersenne primes and non-primes v2 Mickey1 Miscellaneous Math 1 2013-05-30 12:32
possible primes (real primes & poss.prime products) troels munkner Miscellaneous Math 4 2006-06-02 08:35

All times are UTC. The time now is 19:17.


Wed Oct 27 19:17:54 UTC 2021 up 96 days, 13:46, 0 users, load averages: 1.50, 1.43, 1.62

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, 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.