mersenneforum.org  

Go Back   mersenneforum.org > New To GIMPS? Start Here! > Information & Answers

Reply
 
Thread Tools
Old 2017-02-05, 14:26   #1
a1call
 
a1call's Avatar
 
"Rashid Naimi"
Oct 2015
Remote to Here/There

26×31 Posts
Default Largest Known Pair of Consecutive Primes

Hi,
What is the largest known pair of consecutive primes?
This has to be different from largest known twins and gaps. But could be achieved as a research to either.
Thank you in advance.
a1call is offline   Reply With Quote
Old 2017-02-05, 14:38   #2
rajula
 
rajula's Avatar
 
"Tapio Rajala"
Feb 2010
Finland

32×5×7 Posts
Default

I would not be surprised if the pair would be twin primes, since proving those prime is easier than some other candidate pairs. However, possibly there are higher PRP-pairs?
rajula is offline   Reply With Quote
Old 2017-02-05, 15:33   #3
Uncwilly
6809 > 6502
 
Uncwilly's Avatar
 
"""""""""""""""""""
Aug 2003
101×103 Posts

2×33×173 Posts
Default

I suspect the answer you desire lies here.
Uncwilly is online now   Reply With Quote
Old 2017-02-05, 15:54   #4
firejuggler
 
firejuggler's Avatar
 
Apr 2010
Over the rainbow

252910 Posts
Default

what about... mersenne prime? largest gap etc...
firejuggler is offline   Reply With Quote
Old 2017-02-05, 16:01   #5
a1call
 
a1call's Avatar
 
"Rashid Naimi"
Oct 2015
Remote to Here/There

26×31 Posts
Default

Quote:
Originally Posted by Uncwilly View Post
I suspect the answer you desire lies here.
Thank you for the link.
Do they know that their SSL certificate has expired?
a1call is offline   Reply With Quote
Old 2017-02-06, 03:19   #6
axn
 
axn's Avatar
 
Jun 2003

10010111110002 Posts
Default

The answer is most likely #17 & #18 @ http://www.primenumbers.net/prptop/prptop.php

10^999999-172473, 10^999999+593499. aka, largest prime less than million digits and smallest prime with million digits. These are PRPs, of course.
axn is offline   Reply With Quote
Old 2017-02-06, 04:18   #7
a1call
 
a1call's Avatar
 
"Rashid Naimi"
Oct 2015
Remote to Here/There

37008 Posts
Default

Thank you very much for all the replies.
I think it is safe to assume that no such official records are kept.
To me that is a bit of a surprise, given all the exhaustive different categories which are kept track of.
a1call is offline   Reply With Quote
Old 2017-02-06, 08:36   #8
robert44444uk
 
robert44444uk's Avatar
 
Jun 2003
Oxford, UK

192410 Posts
Default

The current prime gap record holder provides two prps which are significantly less large than the pair axn pointed out two posts above. These are currently at positions 530 and 531 in the Lifchitz prp list - 281*499979#/46410-2702372 and 281*499979#/46410+2400766. Strangely enough Henri lists them in reverse size order.

Looking for large prime gaps is perhaps the most inefficient way to getting to a1call's goal. The pair that comprises this large gap took me over 2 months of computer time to discover the prp end points, whereas an average sized gap (about 500,000) with 216849 digits would only take 6 days.
robert44444uk is offline   Reply With Quote
Old 2017-02-06, 17:30   #9
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

22×32×7×37 Posts
Default

Quote:
Originally Posted by robert44444uk View Post
Strangely enough Henri lists them in reverse size order.
Henri's site is likely using sorting everything by "number of digits" (integer; it is equal here), then by description (alphabetically; but alphabetically, "-" is before "+").
Batalov is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Prime Gap Length with consecutive integers divisible by small primes carpetpool Prime Gap Searches 45 2017-09-30 20:51
Unexpected biases in the distribution of consecutive primes axn Lounge 21 2016-06-05 13:00
Largest k*2^n-1 Primes in 2010 Kosmaj Riesel Prime Search 0 2011-01-05 04:24
k's with consecutive small primes gd_barnes Riesel Prime Search 1 2007-07-30 23:26
Largest Simultaneous Primes robert44444uk Octoproth Search 4 2006-02-04 18:45

All times are UTC. The time now is 20:19.

Thu Feb 25 20:19:44 UTC 2021 up 84 days, 16:31, 1 user, load averages: 1.93, 2.00, 1.92

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.