20170205, 14:26  #1 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2·1,153 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. 
20170205, 14:38  #2 
"Tapio Rajala"
Feb 2010
Finland
3^{2}×5×7 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 PRPpairs?

20170205, 15:54  #4 
"Vincent"
Apr 2010
Over the rainbow
19×151 Posts 
what about... mersenne prime? largest gap etc...

20170206, 03:19  #6 
Jun 2003
12463_{8} Posts 
The answer is most likely #17 & #18 @ http://www.primenumbers.net/prptop/prptop.php
10^999999172473, 10^999999+593499. aka, largest prime less than million digits and smallest prime with million digits. These are PRPs, of course. 
20170206, 04:18  #7 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2×1,153 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. 
20170206, 08:36  #8 
Jun 2003
Suva, Fiji
2^{3}×3×5×17 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  281*499979#/464102702372 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. 
20170206, 17:30  #9 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3·3,329 Posts 

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