Mersenne Number Calculator

This Mersenne number calculator works out 2 to the power p, minus 1, for any exponent p you enter, along with two facts that matter in number theory: how many digits the result has and whether p itself is prime. You type in a whole number exponent between 1 and 5000, and the calculator uses exact integer arithmetic to return the full Mersenne number grouped with commas for readability, its digit count, and a yes or no on whether p is prime. This matters because a Mersenne number can only be prime if its exponent is prime; a composite p guarantees the result factors, though a prime p is no guarantee either, since many prime exponents still produce composite Mersenne numbers. Mersenne numbers, named after the French friar Marin Mersenne, sit at the heart of the hunt for record-breaking primes, because an efficient test called Lucas-Lehmer makes checking them for primality far quicker than testing ordinary numbers of similar size, which is why nearly every largest known prime found by the GIMPS project has been a Mersenne prime. Try the default value of 7 for the worked example: 2 to the 7 minus 1 equals 127, a genuine Mersenne prime, then try 11 to see 2047, which factors as 23 times 89. This tool suits students, programmers and anyone curious about number theory, not anyone needing a financial estimate.

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