Quote:
Originally Posted by mart_r
Uhm... What about the twin
(20431926447260679*4001#*(205881*4001#+1)+210)*(205881*4001#−1)/35 +5, +7 (5132 digits)
?

I was not aware of these twin primes. Is the pair listed on a list anywhere, or did you just find the pair, or what? A google search can't find it, and it's not large enough to be on any list I can see. I can confirm with PFGW that they are primes. (the number between the primes is easily trial factored to at least 33.34%)
What about narrowing the definition to twins where at least one of the pair would (at time of discovery) best be proved by general methods like ECPP, (e.g. no N1, N+1, or N1/N+1 combined test is useful) whether they have been proven or are still PRP? Maybe it qualifies for that record!
If not, I give up and admit it's not a terribly interesting twin, it just happens to be the largest I found in my search.