Remark
Although it is known that there are infinitely many prime numbers, we actually only know a finite number of them. At present (June, 1998) the largest known prime number is
This prime number was found by a 19 year old student, Roland Clarkson, January, 1998. Clarkson was one of more than 4000 people joining a large project on the internet to search for so-called Mersenne primes. These are primes of the form
The prime number 23021377 - 1 consists of 909526 digits!
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Prime numbers of the form 2n - 1 are called Mersenne
primes, since they were studied first by Marin Mersenne
(1588-1648).
It is easy to prove that a number 2n - 1 can be prime only
when n itself is a prime. Examples of Mersenne primes are
3 = 22 - 1, 7 = 23 - 1,
31 = 25 - 1, 127 = 27 - 1.
Mersenne found 211 - 1 not to be prime.
Can you find the prime divisors?
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