# 499

This number is a prime.

The smallest prime which is the sum of a prime number
(*p*_{n}) of first odd primes. Note that *n* is
itself the *p*_{m}th odd prime, where *m* is the
smallest prime. [Beedassy]

The decimal expansion of 499^{499} ends with the digits 499499. (Often *p*^{p} ends with the digits of *p*, but this is the only known case for which it ends with the digits of *p* twice.) [Caldwell]

Separate 499 into two (49, 9) and three groups (4, 9, 9) and get two primes after replacing each subset with its square root, namely 73 and 233. Replacing each digit of these latter two primes with their cubes results also in two new primes 34327 and 82727. [De Geest]

The distance light travels the vacuum of space in 499 seconds is approximately the mean distance between the centers of the Earth and Sun (an Astronomical Unit).

499 = 497 + 2 is the reversal of 497 * 2.

The largest prime Köchel number of Mozart's string quartets (String Quartet No. 20 in D). [Hasler]

A Knight's Tour |

The largest 3-digit composite-digit prime. [Loungrides]

The calculated year for the compilation of the astronomical treatise *Āryabhaṭīya* by Hindu mathematician Aryabhata (ar-yuh-BUHT-uh).

Grosswald (1981) proved that if a prime p is greater than
e^{e24} then the smallest primitive root
of p is less than p^{0.499}. [Gudipati]

The smallest prime p for which 2^p and 3^p are both beastly numbers. [Gaydos]

The Scramble Squares Puzzle has 4^9*9! different arrangements of the nine pieces. [Hale]

The smallest prime of the form 5*10^n-1. [Shepherd]

The viewpoint hike at Chimney Rock State Park in North Carolina requires 499 steps.

One hundred factorial is in a prime gap of length 499. [Gaydos]

499 is the sum of an nth perfect number + n (case n = 3). Is there a greater example? [Worrom]

Sum of digits of all primes up to 499 is the smallest bemirp. [Sariyar]