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Old 2018-12-11, 09:08   #2
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Jun 2003

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Originally Posted by enzocreti View Post
I wonder if that is only a coincidence
Yes, unfortunately.

Originally Posted by enzocreti View Post
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.
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