into their prime factors. In abstract algebra, objects that behave in a generalized way like prime numbers include prime elements and prime ideals. A natural...

has no prime factors and is neither prime nor composite. Many properties of a natural number n can be seen or directly computed from the prime factorization...

product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4). Continuing this process until every factor is prime is called prime factorization; the...

(mod 4). Consequently, in the prime factorization of a Mersenne number ( ≥ M2 ) there must be at least one prime factor congruent to 3 (mod 4). A basic...

The prime-factor algorithm (PFA), also called the Good–Thomas algorithm (1958/1963), is a fast Fourier transform (FFT) algorithm that re-expresses the...

multiplicity of the prime factor 2 is 2, while the multiplicity of each of the prime factors 3 and 5 is 1. Thus, 60 has four prime factors allowing for multiplicities...

divisor is 1 is called a prime number. Equivalently, a prime number is a positive integer that has exactly two positive factors: 1 and itself. Any positive...

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...

utility for factoring an integer into its prime factors Factor, a substring, a subsequence of consecutive symbols in a string Authentication factor, a piece...

prime factors. A composite number with two prime factors is a semiprime or 2-almost prime (the factors need not be distinct, hence squares of primes are...

contains the prime factor 3 in its factorization, whereas only one out of every five contains the prime factor 5. All other prime factors, except 2, are...

"Prime Factors" is the tenth episode of Star Trek: Voyager. This television episode is a science fiction story, set in the 24th century of the Star Trek...

Z-factor is a measure of statistical effect size. It has been proposed for use in high-throughput screening (HTS), where it is also known as Z-prime, to...

prime factor of N must lie between 108 and 101000. More generally, if all 2ei+1 have a prime factor in a given finite set S, then the smallest prime factor...

an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is a number in which every prime factor is at most 7. Therefore...

integer to be factored, can be divided by each number in turn that is less than the square root of n. For example, to find the prime factors of n = 70, one...

Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor...

of the prime numbers: for each Fn, choose a prime factor pn; then the sequence {pn} is an infinite sequence of distinct primes. No Fermat prime can be...

will always have characteristic factors or be a prime characteristic factor itself. The number of distinct prime factors of each Fibonacci number can be...

strong primes (e.g. ANSI X9.31), it is necessary but not sufficient that p − 1 has at least one large prime factor. Most sufficiently large primes are strong;...

difficulty of factoring large numbers into their prime factors. Carl Pomerance estimated in 1988 that it would cost $10 million to factor a number with...

of twin prime pair 1657 = cuban prime, prime of the form 2p-1 1658 = smallest composite that when added to sum of prime factors reaches a prime after 25...

a prime number p is a Sophie Germain prime if 2p + 1 is also prime. The number 2p + 1 associated with a Sophie Germain prime is called a safe prime. For...

not in the list, namely, q itself. If q is not prime, then some prime factor p divides q. If this factor p were in our list, then it would divide P (since...

semiprime that is the sum of all the distinct prime numbers from its lower factor through its higher factor The factorial of ten is equal to the product...

constant in an FFT. The prime-factor FFT algorithm is one unusual case in which an FFT can be performed without twiddle factors, albeit only for restricted...

understood to be those numbers that contain a factor of the primorial n#, where n≥13 and is the largest prime factor in the number. Fuller called these numbers...

generate prime numbers efficiently. These are used in various applications, for example hashing, public-key cryptography, and search of prime factors in large...

an odd prime, then every prime q that divides Rp(b) must be either 1 plus a multiple of 2p, or a factor of b − 1. For example, a prime factor of R29 is...

more precisely for prime factors by Legendre's formula. It follows that arbitrarily large prime numbers can be found as the prime factors of the numbers n...