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According to Mersenne 2n - 1 is a Prime number(where n is also a prime number).
As we all know the first prime number is 2 so putting the value of 2 in Mersenne's expression we get 22 - 1 = 3. So, 3 is the first Mersenne prime.
Mersenne expression was considered as a method of finding primes. But it didn't always give prime number. Let us consider an example:
Putting n = 11 in the expression we get 211 - 1 = 2047, but 2047 is not a prime number.
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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.
What are some Mersenne numbers?
A Mersenne number is a number that can be written as 2n - 1. A Mersenne prime is a Mersenne number that is a prime number. Here are some Mersenne primes: 22 - 1 = 3 23 - 1 = 7 25 - 1 = 31 27 - 1 = 127
What are the first 4 mersenne prime numbers?
The first four Mersenne prime numbers are 2, 3, 5, and 7.
Is 1 a mersenne prime?
1 is not a Mersenne prime because 21 - 1 = 2 - 1 = 1 and 1 is not a prime number.
