**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 2**^{n}-1
are called Marsenne's Number. Because a group of prime numbers are of this
form, Prime numbers of the form 2^{n}-1 are called
Marsenne's Primes. Marin Mersenne
(1588-1648) was a French monk who showed that the numbers 2^{n}-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.**
**More Mathematical Recreations** |