Prime Curios!: 499

499
(another Prime Pages' Curiosity)

Curios:

Curios Search: Participate:

The smallest prime which is the sum of a prime number (p_n) of first odd primes. Note that n is itself the p_mth odd prime, where m is the smallest prime. [Beedassy]

The decimal expansion of 499⁴⁹⁹ 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]

It takes approximately 499 seconds for light to travel an astronomical unit (the mean distance between the Earth and the Sun).

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

A knight's tour is a numbered tour of a knight over an otherwise empty chessboard visiting each square once only. A queen placed on the start of a tour discovered by George Jelliss can attack all of the odd primes, and every odd number attacked by the queen is a prime. It is also a more restricted version known as a re-entrant tour, in which the knight, on its 64th move, could arrive back at its starting square. The sum of the odd primes is 499.