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

Emmanuel Vantieghem emmanuelvantieghem at gmail.com
Mon Sep 24 10:55:45 CEST 2018

```These are the next ones :
79, 83, 101, 107, 131, 137, 139, 149, 167, 173, 179, 191, 197, 223, 227,
229, 257

Emmanuel.

Op zo 23 sep. 2018 om 17:52 schreef Tomasz Ordowski <
tomaszordowski at gmail.com>:

> 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, ...
>
> Best regards,
>
> Thomas
> _______
> Consider similar sequences to other bases.
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```