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...