Search results
Results from the WOW.Com Content Network
A regular number has no prime factor above 5 (so it is 5-smooth). ... 88: 2 3 ·11 89: 89: 90: 2·3 2 ·5 91: 7·13 92: 2 2 ... 220: 2 2 ·5·11 221 − 240 221: 13 ...
where n > 1 is an integer and p, q, r are prime numbers, then 2 n × p × q and 2 n × r are a pair of amicable numbers. This formula gives the pairs (220, 284) for n = 2, (17296, 18416) for n = 4, and (9363584, 9437056) for n = 7, but no other such pairs are known. Numbers of the form 3 × 2 n − 1 are known as Thabit numbers.
This article gives a list of conversion factors for several physical quantities.A number of different units (some only of historical interest) are shown and expressed in terms of the corresponding SI unit.
It is the smallest even number with the property that when represented as a sum of two prime numbers (per Goldbach's conjecture) both of the primes must be greater than or equal to 23. [5] There are exactly 220 different ways of partitioning 64 = 8 2 into a sum of square numbers. [6]
Because the set of primes is a computably enumerable set, by Matiyasevich's theorem, it can be obtained from a system of Diophantine equations. Jones et al. (1976) found an explicit set of 14 Diophantine equations in 26 variables, such that a given number k + 2 is prime if and only if that system has a solution in nonnegative integers: [7]
In mathematics, a prime power is a positive integer which is a positive integer power of a single prime number. For example: 7 = 7 1, 9 = 3 2 and 64 = 2 6 are prime powers, while 6 = 2 × 3, 12 = 2 2 × 3 and 36 = 6 2 = 2 2 × 3 2 are not. The sequence of prime powers begins:
For example, the composite number 299 can be written as 13 × 23, and the composite number 360 can be written as 2 3 × 3 2 × 5; furthermore, this representation is unique up to the order of the factors. This fact is called the fundamental theorem of arithmetic. [5] [6] [7] [8]
In number theory, the prime omega functions and () count the number of prime factors of a natural number . Thereby (little omega) counts each distinct prime factor, whereas the related function () (big omega) counts the total number of prime factors of , honoring their multiplicity (see arithmetic function).