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There is a one-to-one relationship between even perfect numbers and Mersenne primes. It is unknown whether there are any odd perfect numbers.

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Q: Are there more mersenne primes known as there are perfect numbers?
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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 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)


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.

Related questions

What is the hundredth perfect number?

It would be extremely large, if it exists.Briefly:It is known that all perfect (even) numbers are generated by the formula 2p−1(2p−1) whenever 2p−1 is prime.When 2p−1 is prime, it is known as a Mersenne prime. There are currently (as of October 2009) only 47 known Mersenne primes, the largest of which has almost 13 million digits.It is unknown if there are further Mersenne primes between the 40th one and the current 47th one.It is unknown if there are infinitely many Mersenne Primes.It is also unknown if there are any odd perfect numbers, but the evidence so far is that the first one to exist must be extremely large.So there may, or may not, be a 100th perfect number.There are only 47 known perfect (even) numbers - one for each of the 47 Mersenne primes.


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 largest known mersenne prime?

There were 47 known Mersenne primes at the beginning of the 21st century, the highest being 43,112,609.


What is the 48th mersenne prime?

As of the current date, November 2011, only forty-seven Mersenne primes are known.


What category of primes is the largest prime?

Mersenne prime is the largest known prime number


Who was Marin Mersenne?

Marin Mersenne (1588-1648) was a monk in France who studied science, especially mathematics. He made some important discoveries in mathematics and musical theory. Some people suggest that his most important contribution to science and mathematics was his correspondence with other scholars. His work on prime numbers of the form 2n-1 resulted in their being known as Mersenne primes.


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 the highest prime factor?

As of 2013, the largest known prime number is 257,885,161 − 1. It is 17,425,170 digits long. There is no largest prime, there is only the largest number that has been shown to be prime. There has been a mathematical proof that no number can be the largest prime since the time of Euclid. No matter how large a prime number is discovered, a larger one exists. The problem is that the larger the primes get, the rarer they get. Just picking a number at random with 20 million digits will almost certainly produce a nonprime number. That is why there are various formulas to give good guesses for prime numbers. The formula for Mersenne numbers Mn=2n − 1. Not all Mersenne numbes are prime, but they have been shown to be good guesses. 257,885,161 − 1 is the 48th Mersenne prime discovered. A Mersenne prime is named after the French monk Marin Mersenne who studied prime numbers in the 17th century.This Mersenne prime and the previous 9 record primes were discovered by the "Great Internet Mersenne Prime Search" (GIMPS), a distributed computing project on the Internet operated just for the purpose of finding Mersenne prime.


Who first found prime numbers?

The Egyptians were the first people to have some knowledge in prime numbers. Though, the earliest known record are Euclid's Elements, which contain the important theorem of prime numbers. The Ancient Greeks, including Euclid, were the first people to find prime numbers. Euclid constructed the Mersenne prime to work out the infinite number of primes.


How many known prime numbers are there?

There are infinite prime numbers as there is infinite numbers. You cannot limit the counting of primes.