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ARPN Journal of Science and Technology >> Volume 7, Issue 2, November 2017

ARPN Journal of Science and Technology


Invited By The Mersenne Primes, The Perfect Numbers And The Mersenne Composite Numbers

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Author Ikorong Anouk Gilbert Nemron, Rizzo Karl Joseph
ISSN 2225-7217
On Pages 50-52
Volume No. 5
Issue No. 1
Issue Date February 01, 2015
Publishing Date February 01, 2015
Keywords Mersenne primes, Mersenne composite, perfect numbers



Abstract

In this paper, via divisibility, we show a simple Theorem which helps to characterize the Mersenne primes, the even perfect numbers and the Mersenne composite numbers. We recall that a Mersenne prime (see [1] or [4] or [5] or [6] or [7]) is a prime of the form Mm = 2m - 1, where m is prime; for example M13 and M19 are Mersenne prime; and Mersenne primes are known for some integers > M19. A Mersenne composite number or a Mersenne composite ( see [2] or [3]) is a non prime number of the form Mm = 2m - 1, where m is prime; it is known that M11 and M67 are Mersenne composite; and Mersenne composite are known for some integers > M67. Finally, we recall that Pythagoras saw perfection in any integer that equaled the sum of all the other integers that divided evenly into it (see [2] ). The ?rst perfect number is 6. Itís evenly divisible by 1, 2, and 3, and itís also the sum of 1, 2, and 3, [note 28, 496 and 33550336 are also perfect numbers (see [2])]; and perfect numbers are known for some integers > 33550336.


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