Number reference
23 explained.
23: twenty-three, prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- twenty-three
- Classification
- prime
- Factors
- 1, 23
- Prime factorization
- 23
- Square root
- 4.795832
- Cube root
- 2.843867
- Binary
- 10111
- Octal
- 27
- Hexadecimal
- 17
- Roman numeral
- XXIII
- Digit sum
- 5
- Digital root
- 5
What makes 23 notable
- Prime. 23 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
23 in everyday use
Human cells carry 23 pairs of chromosomes, so 23 turns up in every genetics textbook. It is the atomic number of vanadium and the jersey number Michael Jordan made famous with the Chicago Bulls. In a room of 23 people there is a better than even chance that two share a birthday, a result so counterintuitive it is known as the birthday paradox. According to Suetonius, Julius Caesar was stabbed 23 times.
Twenty-three is the ninth prime and the first odd prime that is not part of a twin pair, since 21 and 25 are both composite. It is the sum of three consecutive primes, 5 + 7 + 11. In Waring's problem, 23 is one of only two numbers (the other is 239) that need nine positive cubes to be written as a sum of cubes: two 8s and seven 1s.
Nearby numbers
How to read this page
Because 23 is prime, the factor list stops at 1 and 23 itself, so it cannot be shared into equal whole-number groups. That is also what makes it useful as a building block: every larger number with 23 in its prime factorisation inherits it from here.
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