prime number
A prime number is a whole number bigger than 1 that can be split evenly only two ways: by 1, and by itself. Seven is prime — try to share seven cookies into equal piles and you're stuck unless you make one pile of seven or seven piles of one. Six is not prime, because it breaks neatly into 2 × 3.
Primes are the building blocks of all the other whole numbers. Every whole number bigger than 1 is either a prime itself or can be written as a product of primes — and apart from the order you write the factors, there's only one way to do it: 60 is always 2 × 2 × 3 × 5, never anything else. So primes are to arithmetic what atoms are to matter — the pieces everything else is assembled from.
One thing trips people up: the primes never run out. You might think that once numbers get huge they'd all be buildable from smaller pieces, but over 2,000 years ago Euclid proved there are infinitely many primes — no matter how far you count, there's always another waiting.
The first primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, … and 2 is the only even one.
Every other even number is divisible by 2, so 2 stands alone.
Note that 1 is deliberately left out of the primes: if it counted, a number's prime breakdown would no longer be unique (you could keep multiplying by 1). The proof that primes never end appears in Euclid's Elements (c. 300 BCE), and the largest primes we know today — the prize-hunted Mersenne primes — run to tens of millions of digits.