10^49484-10^5384-1,
10^75516-10^2256-1,
10^44304-10^4524-1,
10^68994-10^5814-1 have a 26-31% factored N+1 each.

These 999...9998999...999 numbers are provable with a bit of effort:
each of them needs a 7000-8000-digit helper proven with Primo, and then a Konyagin-Pomerance or CHG proof.

For now, they are PRPs. I am slowly working towards their proof.

To be completed...