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 .)
400 (number) = 2 × 101, Mertens function returns 0, nontotient, noncototient. 405 = 3 × 5, Mertens function returns 0, Harshad number; 406 = 2 × 7 × 29, sphenic number, triangular number, centered nonagonal number, nontotient 407 = 11 × 37, 408 = 2 × 3 × 17 409 is a prime number, Chen prime, centered triangular number. 410 = 2 × 5 × 41, sphenic number, sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number 411 = 3 × 137, self number, 412 = 2 × 103, nontotient, noncototient,