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## Happy October 23

What is so special about October “23”? Well, as Dr. Paul Stanford has proven in his lectures there are interesting facts about every number! Here is what he has to say about the number 23. If you have any other facts to add or if you see any mistakes in my transcription of Dr. Stanford’s notes please use the comments below.

# 23 is…

The largest number not the sum of distinct powers.

With 23 people in a room, odds are that two share a birthday (better than 50:50.)

Prime, smallest odd prime not a twin.

Woodall number. $23=3 \cdot 2^3-1$

One of the only two numbers that need 9 cubes. (The other is 239.)

$23=1^3+1^3+1^3+1^3+1^3+1^3+1^3+2^3+2^3$

If negatives allowed, $23=2^3+2^3+2^3+(-1)^3$

$23=0 \cdot 0!+1 \cdot 1!+2 \cdot 2!+3 \cdot 3!$

23 is the smallest number of rigid rods that brace a square.

First prime where 23rd roots of unity form cyclotomic integers without unique factorization.

Number of trees with eight nodes.

Factor of $2^{11}-1$

$2^{23}-1$ is composite: $47 \cdot 178481$

Sophie Germain prime: 2(23)+1 also prime.

Wedderburn-Etherington number.

The first pillar prime.