42nd Mersenne Prime Probably Discovered 369
RTKfan writes "Chalk up another achievement for distributed computing! MathWorld is reporting that the 42nd, and now-largest, Mersenne Prime has probably been discovered. The number in question is currently being double-checked by George Woltman, organizer of GIMPS (the Great Internet Mersenne Prime Search). If this pans out, GIMPS will have been responsible for the eight current largest Mersenne Primes ever discovered."
Practical Applications/Uses? (Score:5, Insightful)
Re:Mersenne Primes - Definition (Score:5, Insightful)
What an incredibly awesome... (Score:2, Insightful)
Re:Practical Applications/Uses? (Score:4, Insightful)
Communicating with alien species, perhaps.
Mersenne primes have two interesting properties that might catch the attention of alien species: when written in binary, they are entirely composed of '1' bits; and, of course, they are prime.
A sure way to prove to another being that you are intelligent is to spew a bunch of numbers which all happen to be prime. The fact that they can be tranmitted using only '1' bits means the modulation is simple -- just send a series of pulses.
Re:Uses? (Score:5, Insightful)
Re:Uses? (Score:3, Insightful)
Encryption discussions have to take place in a "computing" domain, where a prime only exists if it has been computed to be prime by at least one computer somewhere in the world, and where the prime number can fit on a distribution medium.
Arguing that there are as many Mersenne primes as regular primes is only possible in a theoretical domain in which countably infinite sets can be said to exist.
Re:Uses? (Score:3, Insightful)
Re:Practical Applications/Uses? (Score:4, Insightful)
Re:Uses? (Score:3, Insightful)
1) The number in question really is prime, as you suggested
2) The number in question isn't prime. Then it has prime divisors, none of them in your list (because none of the primes in the list divided our new number).
In both cases, we have derived a way to find at least one new prime from any list of primes, and hence, the collection of primes is non-finite because we can always find "another one".
Re:Uses? (Score:2, Insightful)
You see? For completeness, we say "either N is prime, in which case the list is incomplete, or N is composite, in which case the list is incomplete", and save ourselves worrying about whether N is prime or not.