Largest Known Pair of Consecutive Primes

a1call · 2017-02-05, 14:26

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.

rajula · 2017-02-05, 14:38

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?

Uncwilly · 2017-02-05, 15:33

I suspect the answer you desire lies here.

firejuggler · 2017-02-05, 15:54

what about... mersenne prime? largest gap etc...

a1call · 2017-02-05, 16:01

Quote:

Originally Posted by Uncwilly

I suspect the answer you desire lies here.

Thank you for the link.
Do they know that their SSL certificate has expired?

axn · 2017-02-06, 03:19

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.

a1call · 2017-02-06, 04:18

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.

robert44444uk · 2017-02-06, 08:36

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.

Batalov · 2017-02-06, 17:30

Quote:

Originally Posted by robert44444uk

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 "+").

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2017-02-05, 14:26	#1
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 2³·3³·11 Posts	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.

2017-02-05, 14:38	#2
rajula "Tapio Rajala" Feb 2010 Finland 315₁₀ Posts	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?

2017-02-05, 15:33	#3
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2×3×11×167 Posts	I suspect the answer you desire lies here.

2017-02-05, 15:54	#4
firejuggler "Vincent" Apr 2010 Over the rainbow 2×31×47 Posts	what about... mersenne prime? largest gap etc...

2017-02-06, 03:19	#6
axn Jun 2003 1010101010100₂ Posts	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.

2017-02-06, 04:18	#7
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 2³×3³×11 Posts	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.

2017-02-06, 08:36	#8
robert44444uk Jun 2003 Suva, Fiji 7FA₁₆ Posts	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 - 281499979#/46410-2702372 and 281499979#/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.