Mersenne prime Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. The exponents which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... . If is a composite number then so is . ( is divisible by both and .)
Prime number a product of prime numbers is called a "prime factorization" of the number. For example: The terms in the product are called prime factors. The same prime factor may occur more than once; this example has two copies of the prime factor formula_28. When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for instance, in the second way of writing the product above, formula_29 denotes the square or second power of formula_28. The central importance of prime numbers to number theory and mathematics in general stems from the "fundamental