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 2n ± 1 gave as much trouble and labor as that of 258 + 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 5858 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]