Prime Curios III: The number 23

Number23.jpg
“The Number 23”, a 2007 movie which starred Jim Carrey and was directed by Joel Schumacher.

23 was the number featured in two movies. The 1999 movie called “23” was in German,  starring August Diehl, Fabian Busch, Dieter Landuris, Jan Gregor Kremp. The Hollywood movie called “The Number 23” was released 8 years later, starring Jim Carrey, Virginia Madsen, Logan Lerman, and Danny Huston. Both movies appear to be psychodramas based in some way upon the fear of the number 23, a condition known as Eikositriophobia. The phrase “the 23 enigma” figures in this film, usually uttered by people who find a mystical significance with the number 23.

Yes indeed there are people in the world that fear a specific number of some kind. Each number has its own long and nearly unpronouncable name. The most common fear would probably be Triskaidekaphobia, the fear of the number 13 (oh yeah, another prime number). But let’s stick to the number 23 for this article.

    • It is part of the expression “23 skidoo!”
    • 23 is a number whose digits add to 5, the next prime.
    • 23 is a part of the Birthday Paradox: 23 is the minimum number of people to have in a room, where the probability of two people having the same birthday is just over 50%. Related to this, is the question of how many ways can 23 people be paired? It turns out that this becomes {23 \choose 2} = 253 \approx 365\ln{2}.
    • Twin primes are a pair of prime numbers which are also two consecutive odd numbers. Examples are 3 and 5; 5 and 7; 11 and 13; 17 and 19. The first prime that cannot be “twinned” in this manner is the number 23.
    • 23 is also called a “factorial prime”, because the next whole number, 24, is a factorial: 24 = 4\times 3\times 2\times 1 =4!.
    • Reversing the digits makes it a power of 2: 32 = 2^5=2^{2+3}.
    • e^\pi, rounded down to the next lower integer, is 23, or: \lfloor e^\pi \rfloor =23.
    • The sum of the first 23 primes is 874, a number divisible by 23.
    • 23 is made from digits which are the first two primes, 2 and 3. Wikipedia calls a number like 23 a Samarandache-Wellin prime, where putting together the digits of the first n consecutive primes makes the next Samarandache-Wellin prime. “2” is the first prime, so is the “sum” of only one prime. The second prime has to be the concatentation of the first two primes, so “23” is the next one. 5 divides “235”, so that doesn’t work; but “2357” is prime, the concatenation of the first 4 primes to make the third Samarandache-Wellin prime.
    • 23 is also the number of chromosomes in a human; the atomic mass of sodium; the degrees of tilt of the Earth’s axis; the Bible’s 23rd Psalm; and the number of times Roman emperor Julius Caesar was stabbed in the Theatre of Pompeii.