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18 is a semiperfect number [1] and an abundant number. It is a largely composite number , [ 2 ] as it has 6 divisors and no smaller number has more than 6 divisors. There are 18 one-sided pentominoes .
Number theory was once called arithmetic, but nowadays this term is mostly used for numerical calculations. [15] Number theory dates back to ancient Babylon and probably China. Two prominent early number theorists were Euclid of ancient Greece and Diophantus of Alexandria. [16]
As a biprime with proper divisors 1, 3 and 7, twenty-one has a prime aliquot sum of 11 within an aliquot sequence containing only one composite number (21, 11, 1, 0); it is the second composite number with an aliquot sum of 11, following 18. 21 is the first member of the second cluster of consecutive discrete semiprimes (21, 22), where the next such cluster is (33, 34, 35).
17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number. 17 was described at MIT as "the least random number", according to the Jargon File. [1] This is supposedly because, in a study where respondents were asked to choose a random number from 1 to 20, 17 was the most common choice.
19 is the seventh Mersenne prime exponent. [10] It is the second Keith number, and more specifically the first Keith prime. [11] In decimal, 19 is the third full reptend prime, [12] and the first prime number that is not a permutable prime, as its reverse is composite (where 91 is also the fourth centered nonagonal number).
33 is the 21st composite number, and 8th distinct semiprime (third of the form where is a higher prime). [1] It is one of two numbers to have an aliquot sum of 15 = 3 × 5 — the other being the square of 4 — and part of the aliquot sequence of 9 = 3 2 in the aliquot tree (33, 15, 9, 4, 3, 2, 1).
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This number would be the only known odd perfect number if one of its composite factors (22021 = 19 2 × 61) were prime. [12] 61 is the largest prime number (less than the largest supersingular prime, 71) that does not divide the order of any sporadic group (including any of the pariahs).