[seqfan] Pseudoprime tails of the numbers 2^p - 2

[Tomasz Ordowski]

Dear SeqFans!

Let's define:

Primes p such that the product of all prime factors q >= p of 2^p - 2 is a
Fermat pseudoprime to base 2.

These primes p are unexpectedly many.

Data: 11, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ?

Primes p for which the number 2^p - 2 without the prime factors < p is a
pseudoprime.

The next prime 71 is not in the sequence since 26838337327909507 is not a
pseudoprime [Max Alekseyev].

What are the next terms of this sequence?

Primes that do not have this property are only 2, 3, 5, 7, 13, 71, ...
Please more.

Best regards,

Thomas
_______
Consider similar sequences to other bases.