[seqfan] Re: Safe pseudoprimes to base 2

[Tomasz Ordowski]

P.S. Proof of both conjectures:

Well, I noticed that this pseudoprime is a Cipolla pseudoprime:
http://oeis.org/A210454
Besides, note that (4^q-1)/3 = (2^q-1)(2^q+1)/3 is a super-Poulet number
for every prime q > 3.

Thomas Ordowski

czw., 27 wrz 2018 o 08:21 Tomasz Ordowski <tomaszordowski at gmail.com>
napisał(a):

> Dear SeqFans,
>
> I have an interesting conjecture:
>
> For primes p > 7; if (p-1)/2 is prime, then (2^(p-1)-1)/3 is pseudoprime.
>
> It seems that this pseudoprime is always a super-Poulet number.
>
> How far can you check my guesses?
>
> Best regards,
>
> Thomas
> ____________________
> https://oeis.org/A005385
> https://oeis.org/A001567
> https://oeis.org/A050217
> https://oeis.org/A178997
>