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by Someone
1240 days ago
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> I was looking at a list of prime numbers in binary format and I noticed a pattern, where if 2^n - 1, a Mersenne Prime, is in the list, then (2^(n+1) - 2^(n) - 1) is also in the list. That’s because both are equal. We have 2^(n+1) = 2 × 2^(n) = 2^(n) + 2^(n)
so 2^(n+1) - 2^(n) - 1
= 2^(n) + 2^(n) - 2^(n) - 1
= 2^(n) - 1
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