What Is the Only Even Prime Number? Why It's 2

Q: What is the only even prime number?

The number 2 is the only even prime number. A prime number is a whole number greater than 1 that can be divided evenly only by 1 and itself. Every other even number can also be divided by 2, so it has at least three divisors and can’t be prime. That makes 2 both the smallest prime and the only even one.

What makes a number prime?

Number	Divisors	Prime?
2	1, 2	Yes
3	1, 3	Yes
4	1, 2, 4	No
5	1, 5	Yes
6	1, 2, 3, 6	No
7	1, 7	Yes

Numbers with more than two divisors, like 4 and 6, are called composite numbers.

Is 1 a prime number?

No. It has only one divisor, itself. Mathematicians excluded 1 so that every whole number greater than 1 can be written as a product of primes in exactly one way, a rule called the fundamental theorem of arithmetic. For example, 12 = 2 × 2 × 3.

The first primes

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47…

There are 25 primes below 100.

Infinite primes

Around 300 BC, the Greek mathematician Euclid proved that there are infinitely many prime numbers. His proof is still taught today.

The largest known prime

The biggest known primes are Mersenne primes, of the form 2ⁿ − 1. In October 2024, a volunteer in the GIMPS project found 2¹³⁶²⁷⁹⁸⁴¹ − 1, a number with more than 41 million digits.

Primes in daily life

Online security depends on primes. Encryption systems such as RSA rely on the fact that multiplying two huge primes is easy, but working backward to find them is extremely hard. Every secure website you visit uses this idea; see what HTTPS adds to HTTP.

Unsolved mysteries

Goldbach’s conjecture (1742): every even number greater than 2 is the sum of two primes. It has been checked for enormous numbers but never proven.
Twin prime conjecture: there are infinitely many pairs of primes differing by 2, like 11 and 13.

For another famous number, see what pi is. For a famous number sequence, see what the Fibonacci sequence is.