Number analysis
23
The birthday problem: 23 people give a better-than-even chance of a shared birthday.
The birthday problem: 23 people give a better-than-even chance of a shared birthday.
The number itself
- Value
- 23
- Digits
- 2
- Digit sum
- 5
- Reversed
- 32
- Palindrome
- No
2 + 3
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 32.
Parity and primality
- Parity
- Odd
- Prime
- Yes
- Squarefree
- Yes
- Möbius μ(n)
- -1
- Sophie Germain prime
- Yes — 2n+1 = 47 is also prime
- Nearest primes
- 19 ← → 29
Leaves remainder 1 on division by 2.
Divisible only by 1 and itself.
1 distinct prime factor, 1 with multiplicity.
No prime divides it twice.
(−1) to the power of 1 distinct prime factors.
A gap of 10 between them.
Divisors
- Aliquot sum
- 1
- Classification
- Deficient
1, 23
The proper divisors — everything except n itself.
Its proper divisors fall short by 22.
How many integers from 1 to n share no factor with n.
Sums and additive structure
- Sum of two squares
- No
- Sum of three squares
- No
- Sum of four squares
- Yes
A prime congruent to 3 mod 4 divides it an odd number of times, which rules it out.
Excluded by Legendre: it has the form 4^a(8b + 7).
Lagrange's four-square theorem: every non-negative integer is, without exception.
Shapes and sequences
- Figurate shapes
- None
Not triangular, square, pentagonal, hexagonal, cubic, Fibonacci, Lucas, Catalan, factorial or a power of two.
Digit curiosities
- Happy number
- Yes
- Harshad number
- No
- Collatz trajectory
- 15 steps to 1
Repeatedly summing the squares of its digits reaches 1.
Not divisible by its digit sum 5.
Peaks at 160 along the way.
Written other ways
- Binary
- 10111
- Octal
- 27
- Hexadecimal
- 17
- Base 36
- N
- Roman numerals
- XXIII
- In words
- twenty-three
- Scientific notation
- 2.3 × 10^1
Is 23 a prime number?
Yes. 23 has no divisors other than 1 and itself.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 23 their own way.
- Greek (alphabetic)
- ΚΓʹ
- Babylonian cuneiform
- 𒎙𒐗
- Tamil
- ௨௰௩
References
Further reading: Wikipedia · Wikidata
Notations, naming and the links above come from Wikidata, whose structured data is dedicated to the public domain under CC0-1.0. Retrieved 2026-10-07.