Mersenne Number Calculator

How it is calculated

Enter the exponent p, a whole number from 2 to 1279. The tool computes M(p) = 2p − 1 in exact integer arithmetic and prints every digit with thousands separators; at p = 1279 that is 386 digits. The prime verdict is exact: it comes from the complete list of exponents up to 1279 that give a Mersenne prime (Lucas-Lehmer results): 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607 and 1279. Every other exponent in range is reported as not prime, which includes every composite p, since 2^p − 1 can only be prime when p is prime, and prime exponents such as 11, 23 or 67 that fail. A p below 2, above 1279 or with a fractional part shows no result.

Common mistakes

• Assuming every prime exponent gives a Mersenne prime. p = 11 gives 2,047 = 23 × 89, so it fails, and so does p = 67 (147,573,952,589,676,412,927 = 193,707,721 × 761,838,257,287).
• Entering the number you want to test instead of the exponent. Typing 2047 here is out of range; the field expects p, not 2^p − 1.
• Forgetting the −1 and reading 2^p as the Mersenne number. A power of two above 2 is never prime.
• Expecting results for very large exponents. The tool stops at p = 1279, so the record-sized Mersenne primes with exponents in the millions cannot be checked here and show nothing.