Good stuff Serge,:smile:
Thanks for saving me the hassle. That would have definitely taken me more than a month to find.
Kudos to you sir.
But I think as difficult as it was, it is still a much smaller k than one would have expected for a 10k dd+ (Or is it 13k dd+) twin prime pair if the distribution was unbiased.
I will leave it to Mr. Greathouse to do the probability calculation. It must be about square of the probability getting a single prime of the size.

The sequence [B][URL="https://oeis.org/A126612"]A126612[/URL] [/B]was approved in 2007.
It seems to be missing the [B]M607 [/B]entry, [B]44649[/B].


The additional entries are:

[B]64125, 533040, 407635, 273249 (found by Paul Underwood), 3901012, 718187, 3527063, 9522163, [M21701 entry], 20121642 (found by Batalov), 337342290 (found by Batalov).[/B]


I do not have editing privileges.
what is the process of completing the list?

Thanks in advance.:smile:

For a price of $50 on aws I found this pair, too:
2332724220*(2^86243-1)±1 are prime

[QUOTE=a1call;533147]I do not have editing privileges.
what is the process of completing the list?

Thanks in advance.:smile:[/QUOTE]

If Batalov can vouch for the validity of these new entries he could add them to OEIS.

Ok I will fill in the k value for 21701, and will do a light doublecheck and will submit next week

I am following this thread but have not had the time to properly post to it.
The minimal k.6 for 21701 is
23128315.6.M21701 +/-1
Kudos to Batalov for the 25k dd+ solution.

To post a more complete post for [B]M21701[/B]:
[B]23128315.6.M21701 +/- 1[/B] are minimal Twin-Primes for [B]M21701[/B] with 6541 dd each.
Found using Pari-GP & PFGW.


ETA:

[URL="http://factordb.com/index.php?query=23128315*6*%282%5E21701-1%29%2B1+"]23128315*6*(2^21701-1)+1 [/URL]
[URL="http://factordb.com/index.php?query=23128315*6*%282%5E21701-1%29-1+"]23128315*6*(2^21701-1)-1[/URL]

[QUOTE=GP2;533301]If Batalov can vouch for the validity of these new entries he could add them to OEIS.[/QUOTE]

Thank you [B]GP2 [/B]for letting me know that.
I have a question for you:

i tried to create a Windows server instance on Google-Compute with 96 cores, but I keep getting the message that there is a quota limit of 24 cores for that region. When I check the availability for the region it states that up to 96 cores should be available with the skylake.
How do I setup a Windows instance with 96 cores?

Thank you in advance for your insight.:smile:

[QUOTE=Batalov;533200]For a price of $50 on aws I found this pair, too:
2332724220*(2^86243-1)±1 are prime[/QUOTE]

Again, kudos to [B]Serge [/B]for finding the [B]25972 dd[/B] pair of Twin-Primes.:smile:

I will setup a run for the next Mersenne-Prime in the queue: [B]M110503[/B].
I do not expect a timely resolution. BTW if anyone wants to find Twins for [B] M216091[/B], please be my guest. there are no Twin-Primes for it below 1241000.6.M216091.:smile:

[QUOTE=a1call;533147]The sequence [B][URL="https://oeis.org/A126612"]A126612[/URL] [/B]was approved in 2007.
It seems to be missing the [B]M607 [/B]entry, [B]44649[/B].
[/QUOTE]
I lightly double-checked and posted the correct sequence and some comments. ("various researchers extended sequence"). The sequence is now correct (in the sense: all primes are checked, minimality double-checked for a(1-23); it only takes a couple hours if done optimally).

With regards to individual contributions: The editors' position is that everyone can post only their results, so my comments about others' contributions were edited out. Those who have anything to add are encouraged to [URL="https://oeis.org/wiki/Special:RequestAccount"]register[/URL] and post their own edits.