Prime number
Number theory
A positive integer greater than 1 whose only positive divisors are 1 and itself, equivalently an integer with exactly two distinct positive divisors.
What is usually left out
The exclusion of 1 is a convention with a reason: it makes factorisation into primes unique. If 1 counted, every number would have infinitely many factorisations. Note also that "divisible only by 1 and itself" is false read over all integers, since every prime p is also divisible by −1 and −p.
Related terms
In the atlas
- Twin prime conjecture — Number theory, open
- Goldbach conjecture — Number theory, open