Free Tool

🔢 Prime Number Checker

Explore Prime Numbers & Mersenne Primes

Check if Number is Prime

Enter a number:

Result:

Mersenne primes have the form M_p = 2^p - 1, where p is prime

Enter exponent p (prime):

M_p = 2^p - 1

First 8 known Mersenne primes (only 51 known as of 2023)

M₂ 3 2² - 1

M₃ 7 2³ - 1

M₅ 31 2⁵ - 1

M₇ 127 2⁷ - 1

M₁₃ 8,191 2¹³ - 1

M₁₇ 131,071 2¹⁷ - 1

M₁₉ 524,287 2¹⁹ - 1

M₃₁ 2,147,483,647 2³¹ - 1

Generate primes up to:

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Mersenne primes are primes of the form M_p = 2^p - 1, where p is also prime. Named after French mathematician Marin Mersenne (1588-1648).