What are primes used for?

Primes are used in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. In abstract algebra, objects that behave in a generalized way like prime numbers include prime elements and prime ideals .

What is a prime number?

The concept of a prime number is so important that it has been generalized in different ways in various branches of mathematics. Generally, "prime" indicates minimality or indecomposability, in an appropriate sense. For example, the prime field of a given field is its smallest subfield that contains both 0 and 1.

What is a product of one or more primes?

This theorem states that every integer larger than 1 can be written as a product of one or more primes. More strongly, this product is unique in the sense that any two prime factorizations of the same number will have the same numbers of copies of the same primes, although their ordering may differ.

What is a semiprime number?

A semiprime number is a product of two prime numbers. This is called Lemoine’s conjecture. Every number greater than 1 can be divided by at least one prime number. Every even positive integer greater than 2 can be expressed as the sum of two primes. Except 2, all other prime numbers are odd.