Unique Properties of 23

• 23 is the smallest group of people where there is more than a 50% chance that 2 people will share the same birthday (day and month, not year)
• 23 is the smallest isolated prime, i.e., not an element of a set of twin primes
• 23 is the smallest prime whose reversal is a power: 32 = 2⁵
• 23 is the only prime p such that p! is p digits long
• 23! is the least pandigital factorial, that is it contains all the digits 0 through 9 at least once
• A web page about 23: 23 Enigma in wikipedia
• 23 is the smallest prime p such that the ring of integers in the cyclotomic field of pth roots of unity does not have unique factorization (submitted by Qiaochu Yuan)
• 23 is the smallest Pillai Prime (submitted by Jonathan Vos Post)
• 23 is the smallest home prime that is home to two primes
• 23 is the least positive integer requiring the maximum number of terms, namely 9, when expressed as a sum of positive cubes
• 23 is the smallest prime which is not the sum of two Ulam numbers

Common Properties of 23