# 587

This number is a prime.

The smallest number whose sum of digits exceeds that of its
cube: 587^{3} = 202262003 and 5 + 8 + 7 = 20, while
2 + 0 + 2 + 2 + 6 + 2 + 0 + 0 + 3 = 17. [Beedassy]

Nickel Plate No. 587 (at the Indiana Transportation Museum) is perhaps the best remaining example of a United States Railroad Administration light Mikado steam locomotive.

The number of 10-smooth numbers up to 10^{5}. An
integer is *y*-smooth if all its prime factors is less
than or equal to *y*. [Greene]

Charleston endured 587 days of constant shelling by Federal forces, both on land to the south and at sea near the mouth of the harbor during the U.S. Civil War. [Cambell]

Add 587 zeros between the 9 and the 7 in the prime number 97 to obtain a 589-digit prime.

Let a(1) = 7 and a(n) = a(n-1) + gcd(n, a(n-1)), for n>1. Here "gcd" means the greatest common divisor. Recently, Rutgers graduate student Eric Rowland proved that a(n) - a(n-1) is either 1 or a prime! The differences begin 1, 1, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, .... It is not known if all odd primes occur in this list. Jonathan Sondow found that 587 is the smallest odd prime that does not appear in the first 10000 prime terms.

Computer port 587 is the main alternative port for email. [McCranie]

The number of pages in "The Encyclopedia of Integer Sequences" (revised edition) by N. J. A. Sloane and S. Plouffe. [Beedassy]

587 is the smallest integer for which the first ten digits of its natural logarithm is pandigital (6.375024819). [Gaydos]

587 physicians emigrated to escape the Terror during the French Revolution. [Olry]

The smallest multidigit prime p such that p+1 is a Smith number. [Gupta]

If A = 2, B = 11, C = 17, ... , Z = 281, using the Ramanujan prime alphabet, then 'PRIME' is a Ramanujan prime. [Homewood]