# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## 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
• Hilbert suggested 23 math problems as the challenge for the 20th century
• 23 is the smallest integer that cannot be written as a sum of 8 or fewer positive cubes (the only other number is 239)
• 23 is the smallest prime which is not the sum of two Ulam numbers
• 23 is equal to the product plus sum of the first twin primes, i.e., 3*5 + (3+5) = 23
• 23 is 33 - 22: the difference of the first two consecutive pairs of primes into corresponding powers