23 (number)

23 is a natural number that comes after 22 and before 24. It is an odd number, meaning it cannot be divided by two without a remainder. In Roman numerals it is written XXIII.

23 is a prime number, meaning only 1 and itself divide it evenly. It is the ninth prime number, following 2, 3, 5, 7, 11, 13, 17, and 19.

Mathematical properties

23 has several notable properties relating to prime numbers. It is a safe prime, since 23 = 2 × 11 + 1 and 11 is also prime. It is also a Sophie Germain prime, because 2 × 23 + 1 = 47, which is prime. The sum of its digits (2 + 3) equals 5.

23 relates to factorials: 4! = 24, therefore 4! − 1 = 23, making it one of the numbers known as a factorial prime. Additionally, 23 = 3 × 2³ − 1, which is of the form of Woodall numbers.

Notable example: the birthday problem

In probability theory, 23 appears in what is known as the birthday problem. When 23 people are gathered in a room, the probability that two of them share the same birthday approaches 50%. The surprisingly small number 23 is often counterintuitive to people, which is why this example is used to illustrate how quickly the probability of coinciding events increases.

Application in science and other fields

In biology, a typical human cell contains 23 pairs of chromosomes, totaling 46 chromosomes; reproductive cells (gametes) carry 23 chromosomes each. On the periodic table of elements, atomic number 23 corresponds to the element vanadium.