# 463

This number is a prime. Divide 463 (a prime) by 595 (a palindrome) to obtain an excellent approximation to the common logarithm of 6. The smallest multidigit prime such that both the sum of digits and product of digits of its square remain square. [Russo] 463 meters is exactly one-fourth of an international nautical mile. [Honaker] The entry to the Duomo in Florence, from the Porta della Mandorla on the north side of the Cattedrale di S. Maria del Fiore, contains exactly 463 steps. 463 on a cell phone is the numbers pressed to spell God. [Gregor] The first prime whose digits form a scalene triangle with the smallest prime perimeter. [Beedassy] The first in the smallest set of 7 consecutive primes (463, 467, 479, 487, 491, 499, 503) that are congruent to 3 (mod 4). [Post] The smallest prime that is a sum of mountain primes, i.e., 463 = 131 + 151 + 181. [Loungrides] There is a 4-6-3 double play in baseball. [Homewood] According to "The Empty Hexagon Theorem," a result established by V. A. Koshelev guarantees that 463 random points on a plane (no three concurrent) determine the vertices of an empty convex hexagon. [Beedassy] The number of days in the synodic period of Ceres. [Homewood] A 463-tuple would be an "interesting constellation." Largest known odd prime p that divides 0! - 1! + 2! - 3! + 4! - . . . + (p-1)!. [Sondow] The only distinct-digit 3-digit prime which remains a prime after a prime digit is subtracted from any of its digits or from all of its digits simultaneously, i.e., 263, 443, 461, 241. [Loungrides] The smallest prime number that is the sum of divisors of an abundant number (392). [Gaydos]

(There is one curio for this number that has not yet been approved by an editor.)