23

23
Basic Information
Cardinal Number	twenty-three
Ordinal Number	twenty-third
Roman Numeral	XXIII
Greek Numeral	ΚΓ´
Factorization	23
Standard Form	2.3 × 101
Different Representations
Binary Form	101112
Ternary Form	2123
Quaternary Form	1134
Quinary Form	435
Senary Form	356
Septenary Form	327
Octal Form	278
Nonary Form	259
Undecimal Form	2111
Duodecimal Form	1B12
Tridecimal Form	1A13
Quattuordecimal Form	1914
Quindecimal Form	1815
Hexadecimal Form	1716
Septendecimal Form	1617
Octodecimal Form	1518
Novemdecimal Form	1419
Vigesimal Form	1320
Unvigesimal Form	1221
Duovigesimal Form	1122
Trevigesimal Form	1023
Quattuorvigesimal Form	N24
Quinvigesimal Form	N25
Hexavigesimal Form	N26
Septenvigesimal Form	N27
Octovigesimal Form	N28
Novemvigesimal Form	N29
Trigesimal Form	N30
Untrigesimal Form	N31
Duotrigesimal Form	N32
Tretrigesimal Form	N33
Quattuortrigesimal Form	N34
Quintrigesimal Form	N35
Hexatrigesimal Form	N36
Previous	19
Current	23
Next	29

23 is a prime number from 1-100. 23 has two factors, 1 and 23. 23 is the ninth prime number, and the ninth prime number from 1-100. The primorial of 23 is 223,092,870.

Proofs

• — 23 is divisible by 1

• — 23 is not divisible by 2-22

• — 23 is divisible by 23

• Therefore, 23 has 2 factors and is prime.

As an Exponent of Mersenne Number

2²³ - 1, which is the number 8,388,607, can be factored into 47 x 178,481, meaning it is not a prime number.

Relationships with other odd numbers

The numbers before

• 17 is the second previous prime number.
  • The difference between 23 and 17 is 6. Therefore, they are sexy primes.
• 19 is the previous prime number.
  • The difference between 23 and 19 is 4. Therefore, they are cousin primes.
• The previous odd number, 21, is the third odd composite number. It is divisible by 3 and 7.

The numbers after

• The next odd number, 25, is a square number: 5² = 25.
• 27, the odd number following 25, is a cube number: 3³ = 27.
• 29, the odd number following 27, is a prime number.
  • The difference between 29 and 23 is 6. Therefore, they are sexy primes.

Trivia

• 23 is in the only sexy prime quintuplet (5, 11, 17, 23, 29) since all multiples of 5 (except itself) are composite numbers.
• 23 is not a part of a twin prime pair. This means it is an first isolated prime.
• There are only three consecutive prime numbers that end with the same last digit and are separated by 10, they are [3,13,23]. After that, it becomes impossible because every 3rd positive integer is composite since it is a multiple of 3.

Prime Numbers 1-1,000