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 .)
Weakly prime number Weakly prime number In number theory, a prime number is called weakly prime if it becomes not prime when any one of its digits is changed to every single other digit. Decimal digits are usually assumed. The first weakly prime numbers are: For the first of these, each of the 54 numbers 094001, 194001, 394001, ..., 294009 are composite. A weakly prime base-"b" number with "n" digits must produce ("b"−1) × "n" composite numbers when a digit is changed. In 2007 Jens Kruse Andersen found the 1000-digit weakly prime (17−17)/99 + 21686652. This is the largest known weakly prime number