Composite number

A composite number is a positive integer greater than one that can be expressed as a product of two smaller positive integers. It has at least one positive divisor other than one and itself.

Prime number: A positive integer greater than one whose only positive divisors are one and itself. Unlike a composite number, a prime has no factorization into smaller positive integers.
Trial division: A method for testing divisibility by candidate factors in sequence. Checking possible divisors up to the square root can establish compositeness.
RSA (cryptosystem): A public-key cryptosystem whose security relies on the difficulty of factoring large integers. RSA public keys are built from products of large prime numbers.
Perfect power: An integer greater than one expressible as an integer power with exponent at least two. Perfect powers form a special subset of composite numbers with repeated factors.
Divisor: An integer that divides another integer evenly, leaving no remainder. A composite number has a divisor strictly between one and itself.
Square root: A number which, when multiplied by itself, gives a specified number. A composite integer has a factor no larger than its square root.
Integer factorization: The problem of expressing an integer as a product of smaller integers, usually primes. Factoring is the central computational task associated with composite integers.
Square-free integer: An integer not divisible by the square of any prime. A composite number can be square-free or have repeated prime factors.
Prime factorization: The expression of an integer as a product of prime numbers. It breaks every composite number into its fundamental multiplicative factors.
Factor pair: Two numbers whose product equals a specified number. Any factor pair of a composite number witnesses its compositeness.

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