So Alice communicates her product to Bob, keeping her factors secret.

Mersenne Primes are numbers of the form 2p-1, where p is prime. Suppose that Alice and Bob wish to communicate secretly over the internet.

Prime factors therefore represent a fundamental and unique decomposition of a given positive integer.

RSA numbers are composite numbers having exactly two prime factors i. This is a special number called a Mersenne Prime, named after a 16th Century Monk who was a theologian, philosopher, music theorist and mathematicion, though many disagree about his fame as a mathematician.

The larger the numbers, the safer the encryption.

In fact, the new prime is so large that — at present — no conceivable technological advancement in computing speed could lead to a need to use it for cryptographic safety.

It starts with 2 then 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 and so on.

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MathWorld News: RSA Factored