Since this applies to every prime p, we conclude that there is no largest prime and the prime sequence runs on forever.Since we have no way of producing primes at will, there is, at any one time, alargest known prime and nowadays the champion is always a Mersenne prime, thanks to the international GIMPS venture(Great Internet Mersenne Prime Search). This is a collaborative project of volunteers, which began in 1996. The project uses thousands of personal computers working in parallel,which test Mersenne numbers for primality using a specially devised cocktail of tailor-made algorithms. The current world champion, announced in August 2008, is 2p-1 where p=43,112,609, although a new Mersenne prime was found in April 2009 with p=42,643,801. These numbers have about 13million digits and would take thousands of pages to write down in ordinary base ten notation.