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Two is a Mersenne prime because it follows the algorithm 2n - 1 to produce the Prime number 3 (22 - 1 = 4 -1 = 3).
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Mersenne primes can be defined in two equivalent ways:
Numbers of the form 2n - 1 where n is a prime
or where the number 2n - 1 is itself a prime.
The more commonly accepted definition is the second one. Thus n = 2 gives the smallest Mersenne prime, which is 3.
But, since n = 2 gives a result that is prime, it is also sometimes referred to as a Mersenne prime.
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What is the difference of mersenne prime and a prime number?
A prime number has only two factors, 1 and itself. A Mersenne prime is a prime number derived from the algorithm 2n - 1. For example, 23 - 1 = 7 and 7 is a prime number so 3 is a Mersenne prime. Similarly 27 - 1 = 127 and 127 is a prime number so 7 is a Mersenne prime. There are 47 known Mersenne primes, the highest being 43,112,609.
What is the definition of Mersenne numbers?
A Mersenne number is a number of the form 2n-1. When this number is prime, it is known as a Mersenne prime.A Mersenne prime has the form 2n-1. For 2n-1 to be prime, n must also be prime. Examples are the Mersenne prime 7 (23 - 1 = 7) and the Mersenne prime 127 (27 - 1 = 127)
What is special about a Mersenne prime?
A Mersenne prime has the form 2n-1. For 2n-1 to be prime, n must also be prime. Perfect numbers have the form 2n-1(2n-1) where 2n-1 is a Mersenne prime, so when a new Mersenne prime is discovered, another perfect number is also found.
Is 1 a mersenne prime?
1 is not a Mersenne prime because 21 - 1 = 2 - 1 = 1 and 1 is not a prime number.
What are Mersenne Primes used for?
Mersenne primes are mostly of interest as mathematical curios. A Mersenne prime has the form 2n-1. For 2n-1 to be prime, n must also be prime. Perfect numbers have the form 2n-1(2n-1) where 2n-1 is a Mersenne prime, so when a new Mersenne prime is discovered, another perfect number is also found.
