prime number
A prime is a whole number that cannot be broken into a rectangle of dots wider than one row — 7 pebbles can only be laid out as a single line of 7, never as a tidy grid. Primes are the atoms of multiplication: numbers that refuse to split into smaller factors.
Precisely, a prime number is an integer greater than 1 whose only positive divisors are 1 and itself. The first few are 2, 3, 5, 7, 11, 13, 17, 19. Note that 2 is the only even prime, since every other even number has 2 as an extra factor. The number 1 is deliberately not counted as prime — including it would wreck the uniqueness of prime factorization.
Primes never run out: Euclid proved there are infinitely many of them, and his short argument is one of the oldest gems in mathematics. They thin out as numbers grow, yet they keep appearing forever, which is why so much of number theory orbits around questions about how they are distributed.
Is 91 prime? Test small primes: 91 = 7 times 13. Since it has a factor other than 1 and 91, it is not prime — it is composite.
To check primality, trial-divide by primes up to sqrt(n).
Why exclude 1? If 1 were prime, then 12 could be written as 2·2·3 or 1·2·2·3 or 1·1·2·2·3 — uniqueness of factorization would fail. So 1 is called a unit, neither prime nor composite.