Multiple choice general knowledge math & puzzles

The numbers 3, 7, 31, and 127 are what?

  1. Mersenne Primes

  2. Leibniz Primes

  3. fermat Primes

  4. Newton Primes

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A Correct answer
Explanation

These are Mersenne primes, which are primes that can be written in the form $M_n = 2^n - 1$. For $n=2, 3, 5, 7$, we get $3, 7, 31, 127$. Fermat primes follow the form $2^{2^n}+1$.