According to the enviable people at News Scan, "Mersenne primes are an especially rare breed that take the form of 2-to-the-power-of-P, where P is also a prime number".

Well, I suppose that's partly correct: primes of the form 2-to-the-power-of-P are somewhat rare. They aren't all that hard to find, though. See the whole article here.

I shouldn't complain too much. The normally reliable folks at Mathworld (sponsored by New Kind of Scientist, Stephen Wolfram Andhart), persist in claiming in their article on Prime Numbers, that "no efficient algorithms are known for factoring arbitrary primes". As it happens, I know a great algorithm for factoring arbitrary primes, which works about as fast as it is possible to work.

That had better be all for now.