# 233

This number is a prime. 233 is an interesting Fibonacci prime. If divided by the Fibonacci number 144, it approximates the golden ratio. The smallest prime factor of 229 - 1. 2233 - 3 is prime. [Kulsha] Describing 233 and repeating the process with each new term produces five more primes, i.e., "one 2, two 3's," generates 1223, etc. [Rivera] Neil J. A. Sloane, editor-in-chief of the On-Line Encyclopedia of Integer Sequences, works at AT&T Shannon Laboratories in room C233. The only known multidigit Fibonacci prime whose digits are all Fibonacci primes. [Gupta] The only known Fibonacci prime whose sum of digits is a Fibonacci number. [Russo] "Pascal's Wager" appears in Pensées 233. Had Ray Bradbury used the metric system, he may have called his novel "Celsius 233." [Hartley] Claimed to be the first book with no verbs, The Train from Nowhere by Michel Thaler (a pseudonym) has 233 pages. [Opao] 233 is the final chapter of The Curious Incident of the Dog in the Night-Time by Mark Haddon, which uses all prime numbers for its chapters. 233+(2+3+3), 233+2*3*3, and 233+2^3*3 are consecutive primes. [Silva] The smallest prime in base-3 whose sum of digits is composite. The smallest magic constant of a 5-by-5 prime magic square:

```
41  11   79   19   83

31  67   29   89   17

61  59   05   71   37

97  53   13   47   23

03  43   107  07   73

```
Note that this solution includes all the twenty-four odd primes below hundred (Andrew Lelechenko, 2009). [Beedassy] Jewel Cave in South Dakota contains 233 kilometers of mapped passageways. [Robinette] The largest known Fibonacci prime with exactly two different digits. Note the first two primes. [Capelle] 233 is the sum of the squares of first four semiprimes. Note that its reversal is the sum of the squares of three consecutive even semiprimes: 332 = 6^2 + 10^2 + 14^2. [Silva] 2*3*5* ... *prime(233 - 1) = prime(233) - 1 (mod prime(233)). Note that 233 is the smallest known prime with this property and there exist only one other known such prime. [Firoozbakht] The smallest Fibonacci prime whose index is a perfect number. [Pol] "The triangular theorem of eight and non-finiteness results for quadratic polynomials" by Wieb Bosma and Ben Kane conjectures that the largest of all values in a sequence related to Universal Quadratic Forms, the representability of integers as sums of triangular numbers, and the 290-Theorem, is 233. [Post] The larger of only two primes less than a googol formed by concatenating a number n followed by n 3's. The other is 13. [Loungrides] If A=1, B=2, C=3..., Z=26 then 'A RIGHT-TRUNCATABLE PRIME' is a right-truncatable prime. [Homewood] The sum of the first five distinct-digit reflectable primes {3, 13, 31, 83, 103} is 233. Note that π(3) + π(13) + π(31) + π(83) + π(103) = 23*3. [Worrom] 233 divides 239*241*251*257 + 1. Can you find five larger consecutive primes p < q < r < s < t such that p|qrst + 1? [Loungrides] The smallest prime-digit prime that is the sum of three prime-digit primes (3+7+223). [Loungrides] The only multidigit prime-digit Fibonacci prime. [Loungrides] The Woolworth Building is an early American skyscraper (once the world's tallest) located at 233 Broadway in Manhattan, New York City. [Gilbert] The smallest prime and the only known prime-digit prime that can be represented as the sum of eleven consecutive primes, i.e., 5 + 7 + 11 + ... + 37 + 41. [Loungrides] A potentially rocky planet, known as Barnard's star b, is a 'super-Earth' that orbits around its host star once every 233 days. Roman Opalka's artwork called "OPALKA 1965/ 1-∞" consists of large size canvases, 233 in all, on which were written all numbers from 1 to 5607249. [Olry] Meteor Crater is off Exit 233 in Winslow, Arizona. [Hooper] 233 is the smallest number that can be written as the sum of 11 primes in 11 ways. Is there another prime which can be the the sum of p (prime) distinct primes in p ways? [Sariyar] The James Webb Space Telescope must operate at the negated value of 233 Celsius. [Harrison]

(There are 11 curios for this number that have not yet been approved by an editor.)