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[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. [3] [4] E.g., the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7 but the integers 2 and 3 are not because each can only be divided by one and itself ...
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 list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
A related concept is that of a largely composite number, a positive integer that has at least as many divisors as all smaller positive integers. The name can be somewhat misleading, as the first two highly composite numbers (1 and 2) are not actually composite numbers; however, all further terms are.
For any possible exponent, whichever integer has the greatest ratio is a superior highly composite number. It is a stronger restriction than that of a highly composite number, which is defined as having more divisors than any smaller positive integer. The first ten superior highly composite numbers and their factorization are listed.
Euler's proof of the zeta product formula contains a version of the sieve of Eratosthenes in which each composite number is eliminated exactly once. [9] The same sieve was rediscovered and observed to take linear time by Gries & Misra (1978). [19] It, too, starts with a list of numbers from 2 to n in order. On each step the first element is ...
In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the same base. In the case of numbers that are not square-free , the factorization is written without exponents, writing the repeated factor as many times as needed.