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MARSENNE'S PRIMES

Prime numbers are positive integers greater than one with no factors other than one and themselves.  They include 2, 3, 5, 7, 11, 13, 17 ...  With the exception of two, all the prime numbers are odd numbers.

A number of the form 2n-1 are called Marsenne's Number.  Because a group of prime numbers are of this form, Prime numbers of the form 2n-1 are called Marsenne's Primes.  Marin Mersenne (1588-1648) was a French monk who showed that the numbers 2n-1 were prime for n=2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257.  It can be noted that all these numbers are prime numbers.  It was later shown that in order for a Mersenne number to be a Mersenne prime, n has to be a prime number.

Mersenne's prime has also been an area of interest because it has been noted that every Mersenne's prime corresponds to a one perfect number thru the relationship

          p = 2(n-1)(M)

where p is the perfect number and (M) is a Mersenne's prime.

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