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Old 2004-02-28, 15:41   #11
mfgoode
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Jan 2004
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Default non mersenne primes.

Quote:
Originally Posted by jinydu
It is not always true that (2^M)-1, where M is a mersenne prime, is itself prime. MM15 and MM31 are not prime.
:



You have brought up an interesting point on Mersenne primes.
However your comment bears no relevance to the topic under discussion. Ron clearly states about “non mersenne” primes and primes formed from factorials.
That’s why I have referred him to Wilsons theorem and given the link to explore further.
As a ready reference Wilsons theorem states that for any prime one has the formula
(p-1)! = -1 (mod p). This is not true if p is composite and must be prime.
For larger primes this formula is not practical and involves a lot of computation even for a computer. That’s why Mersenne prime formulae are preffered over Wilsons. At the same time Wilsons theorem is both necessary and sufficient for primality. As the number of primes is infinite and this formula involves primes it gives an infinite number of results.

Mally.
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