Quote:
Originally Posted by enzocreti
I wonder if that is only a coincidence
|
Yes, unfortunately.
Quote:
Originally Posted by enzocreti
What is the probability to have by mere chance two probable primes with these two amazing exponents?
|
This question is not very meaningful. You haven't specified what property(ies) of this pair of numbers makes them "amazing". Once you specify that in a more mathematically rigorous way, we can attempt to quantify the probability.
As such, what you're doing is looking for after-the-fact coincidences. When you started out with this series, you were only focusing on the lack of 6 (mod 7) primes. Now you're focusing on pairs of "amazing" exponents. But none of these were predicted beforehand. You just looked at the numbers (which gives primes) and tried to find coincidences, and you did. Nothing more.