Generalization
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The binary representation of 2p − 1 is the digit 1 repeated p times, for example, 25 − 1 = 111112 in the binary notation. A Mersenne number is therefore a repunit in base 2, and Mersenne primes are the base 2 repunit primes.
The base 2 representation of a Mersenne number shows the factorization pattern for composite exponent. For example:
Read more about this topic: Mersenne Prime