# 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 2^{29} - 1.

2^{233} - 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 73Note 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]

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]

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]