# 58

This number is a composite.

58 is the sum of the first seven prime numbers.

In 1869, Landry wrote that no one of the numerous factorizations
of the numbers 2^{n} ± 1 gave as much trouble
and labor as that of 2^{58} + 1.

The smallest Smith number with a prime sum of digits. Note also that its digits and their sum are a sequence of Fibonacci numbers. [Necula]

The 58th Lucas number plus 58^{58} is prime. This is the largest such number less than a thousand. [Opao]

58 is a Hoax Number. 58 reversed (85) is a Hoax Number and 85 = 5 x 17. Note that 5 x 71 = 355 is also a Hoax Number. [Andrew]

The only double-digit number such that 58^n+85^n is prime for n=2, 4, 16, i.e., for three powers of 2. [Loungrides]

Exactly half of the first 58 "Lunatic numbers" are prime in the traditional sense. [Gaydos]