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History Of The Perfect Number Essay

865 words - 4 pages

The perfect number is a positive integer that is equal to the sum of its proper divisors. Earlier definitions of a perfect number were 'aliquot parts' of a number. An aliquot part means a proper quotient of a number. According to Webster’s dictionary, the term perfect number was first used in the 14th century. The discovery of such numbers was lost in prehistory. The smallest perfect number is six. It is the sum of its divisors one, two, and three. Other perfect numbers are twenty-eight, 128, and 496. In the paragraphs below I will talk about the history of the perfect number and Euclid’s theorem and the founder of the perfect number.
The first four perfect numbers were known to the ancients ...view middle of the document...

“As many numbers as we please beginning from unity be set out continuously in double proportion until the sum of all becomes prime, and if the sum is multiplies by the last the producer will be perfect.” p. 131
Euclid’s Theorem, also known as Mersenne organization, was said that any number given in the form of 2^n-1(2^n-1) is perfect when 2^n-1 is a prime number. A number in this form is called a Mersenne number. Every perfect number and even number has been found to fit this formula. Where “n” is located in the formula, a very short list of prime numbers can take the place and they make up Mersenne’s prime numbers. Euclid was the discoverer of this theorem. In the 18th century Leonhard Euler showed that any number must be obtainable in Euclid’s theory.
The significant study of the perfect number was by Nichomachus of Gerasa. Nichomachus said all perfect numbers end in six and eight. Euclid’s theorem is true; there are no negative perfect numbers. All perfect numbers are even and there are infinitely many perfect numbers. Perfect numbers were said to have important number properties by the ancient Greeks. Perfect numbers are connected with Mersenne prime numbers, which are number that are prime (a natural number that can only be divided by one or itself) and in the form of Mp=2^p-1.
Euclid of Alexandria may have been the first to discover numbers that were both prime and infinite. It is known now that all...

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