this post was submitted on 21 Oct 2024
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I don't know if this is a common feature of large primes, but the digits in the exponent (136,279,841) themselves represent a prime number.
that does happen to be one of the defining characteristics of mersenne primes.
And searching for mersenne primes happens to be the easiest known way to find extremely large prime numbers (via the Special Number Field Sieve I believe)