Cunningham Chains Revisited

I've already discussed Cunningham chains in an earlier post but today I was 24496 days old and an analysis of the this number led me to a record-breaking example of such a chain. The factors or 24496 are \(2^4 \times 1531\) and \(1531\) turns out to be the smallest prime that leads to a Cunningham chain of the second kind (\(2p-1\)) with a length of \(5: 1531, 3061, 6121, 12241, 24481\)

• 2131 holds the record for length 4 (2131, 4261, 8521, 17041)
• 2 holds the record for length 3 (2, 3, 5)
• 7 holds the record for length 2 (7, 13)
• 11 holds the record for length 1 (11 only)

These numbers (11, 7, 2, 2131 and 1531) form the first five terms of OEIS A109828. The subsequent five terms are 385591, 16651, 15514861, 857095381 and 205528443121.