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How many Mersenne prime numbers are there?
It is, as of now, an open question whether there are a finite or an infinite number of Mersenne primes. At the beginning of the 21st century there were 47 known Mersenne primes, the highest being 43,112,609.
How many perfect numbers are known?
So far 47. Euler proved that every even perfect number will be of the form 2p−1(2p−1), where p is prime and 2p−1 is also prime. If 2p−1 is prime it is known as a Mersenne prime. Since 47 Mersenne primes are known, 47 even perfect numbers are known. As for odd perfect numbers, none are known, nor has it been proven yet that there aren't any.
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 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.
Who came up with Prime numbers?
Primes were known to the early Greek Mathematicians - the Pythagoreans about 400BC and Euclid about 300BC. Eratosthenes came up with 'the sieve of Eratosthenes' for working out primes about 200BC. There is no record that the Babylonians knew about primes.
