Sieved with srsieve2cl, PRP-tested with mprime (base 3).
Checked with pfgw using bases 5 and 7.

These numbers are also equal to the form 2*k*R(270343)+1, which are candidates for factors of the double Repunit number R(R(270343)). But none of the found PRPs is a factor of R(R(270343)).

To be completed...