In mathematics and more precisely in modular arithmetic, a Mersenne prime is a prime number being written in the form 2^p - 1, p being first.
These primes are named after French mathematician and a scholar of the seventeenth century, Marin Mersenne. Mersenne primes are in base 2 (binary).
Mersenne primes are related to perfect numbers, which are numbers equal to the sum of their proper divisors. It is this connection that has
historically driven the study of Mersenne primes. From the fourth century BC, Euclid proved that if M = 2^p - 1 is prime,
then M (M +1) / 2 = 2 (p-1) (2p - 1) is a perfect number. Two millennia later, in the eighteenth century, Euler proved that all even
perfect numbers have this form. No odd perfect numbers are known.
Run Date : 02-Jan-2011 00:47 UTC (Jan 01 2011 19:47 EST)
Last Primenet Report Date : 02-Jan-2011 00:00 UTC
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Prime numbers are fascinating topic for all interested in numbers in general and in Mersenne games in particular. Because if it is fun for you to play with numbers, all get simple. Otherwise it is boring. For example let's consider the case of roulette, whetherer you play a game of roulette or simply pretend to play the game. Obviously you do not need to master prime numbers to understand this game as there are only 32 numbers to choose from in this game. But the question is rather, is there any way to predict the outcome of that game. This is what thousands of people have been trying to do since the apparition of this game a few hundred years ago, and interestingly the point here is that prime numbers may help to answer this gaming question, as well as chaos theory.