Should I take over ...?

[Cybertronic]

Originally Posted by Andrew Usher

Yes, it seems so. It's looking better already, though obviously not finished. I must note again (I already did in the prime-gap thread) that Nicely's prime-gaps page must now be linked as https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html , not anywhere on trnicely.net , which no longer contains anything useful. The list is not in a very readable format as e.g. on the Wikipedia page 'Prime gap', and you may wish to consider re-doing it similarly.

Your link to Nicely's page is exactly mentioned here.
https://pzktupel.de/RecordGaps/GAP01FO.html

I have only collect the first occurrence...not 1st known....
Okay, I have also added here: https://www.pzktupel.de/JensKruseAndersen/risinggap.php

Also, for 'smallest' records, be clear about whether it is known to be the smallest (exhaustively searched) or just the smallest known. The wording you used, 'smallest existing' presumably means the former but is awkward and could easily be taken as a non-native speaker's error for the latter.

Do you mean the smallest prime k-tuplets with n-digits ?
Which link ?

[Andrew Usher]

The gap records page you just added is the more-readable format I mentioned; thanks for that, I hadn't seen the extended list before, even though I'm sure I visited Andersen's site. As you likely know, the next two after Nicely's list are probable record gaps as well.

(remaining details moved to PM)