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This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes.
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. [1] [2] Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit.
Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS). There are many special types of prime numbers. A composite number has Ω(n) > 1.
The Rhind Mathematical Papyrus, from around 1550 BC, has Egyptian fraction expansions of different forms for prime and composite numbers. [14] However, the earliest surviving records of the study of prime numbers come from the ancient Greek mathematicians, who called them prōtos arithmòs (πρῶτος ἀριθμὸς).
The following other wikis use this file: Usage on arz.wikipedia.org ستانيسلاف كنابوسكى; Usage on azb.wikipedia.org ساده عدد
Hence, for a highly composite number n, the k given prime numbers p i must be precisely the first k prime numbers (2, 3, 5, ...); if not, we could replace one of the given primes by a smaller prime, and thus obtain a smaller number than n with the same number of divisors (for instance 10 = 2 × 5 may be replaced with 6 = 2 × 3; both have four ...
The number 1 has only a single factor, itself; each prime number has two factors, itself and 1; composite numbers are divisible by at least three different factors. Using the size of the dot representing an integer to indicate the number of factors and coloring prime numbers red and composite numbers blue produces the figure shown.
The article uses the terms daughter and parent to describe composites and the primes that they lead to, with numbers leading to the same home prime called siblings (even if one is an iterate of another), and calls the number of iterations required to reach a parent, the persistence of a number under the map to obtain a home prime, the number of ...
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