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perfect numbers |
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A number is perfect (or deficient or abundant) as it is equal to (or less or more) than the sum of its aliquot parts (its factors). For example, 6 is perfect as 6=1+2+3; 8 is deficient as 8>1+2+4 or 12 is abundant as 12=1+2+3+4+6. Euclid proved (in Elements IX, 36) that if
Fibonacci (1202) draw a rule whereby
a rule which holds for all known perfect numbers. The fifth perfect number is given as 33 550 336 in an anonymous manuscript in 1456-1461. The Pythagoreans used this term in another sense, because apparently 10 was considered by them to be a perfect number. Proposition 36 of Book IX of Euclid's Elements is:
Perfect number appears in English in 1570 in Sir Henry Billingsley's translation of Euclid.
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Mersenne's Primes and Perfect Numbers See Eratosthenes' Prime Number sieve and download some worksheets: 100, 200 or 500 number sieve. What people thought of primes through the history Prime number (as the one defined by Aristotle, Euclid and Theon of Smyrna) is a number "measured by no number but by an unit alone" Iambilicus said that a prime number is also called "odd times odd". Prime number was apparently first described by Pythagoras. Iamblichus writes that Thymaridas called a prime number rectilinear since it can only be represented one-dimensionally. In English prime number is found in Sir Henry Billingsley's 1570 translation of Euclid's Elements (OED2). Some older textbooks include 1 as a prime number. In his Algebra (1770), Euler did not consider 1 a prime [William C. Waterhouse]. Learn something more about perfect numbers by looking at abundant and deficient numbers page.
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