1597
This number is a prime.
The largest known Fibonacci emirp.
2^1597 + 2^1583 + 2^1579 + ... + 2^11 + 2^7 + 2^5 + 2^3 + 2^2 + 1 is prime. [Patterson]
The largest of 29 consecutive primes of the form 2n2 + 29 for n = 0 to 28. [Terr]
There exist positive values of n such that the square root of 1597n2 + 1 is an integer, but you'll need more than a hand-held calculator to find even the smallest solution.
Jacopo Peri (1561-1633) wrote the first work to be called an opera today, Dafne (circa 1597, now lost). Note that 1597 is the arithmetic mean between 1561 and 1633.
The largest known Fibonacci prime with only odd digits. It
has also more distinct odd digits than the others. [Capelle]
The 1st American Edition (2009) of SCIENCE: The
Definitive Visual Guide by DK Publishing, contains a list of the first 918
prime numbers on page 475. Well, almost; one of the primes
(the intended 1597) is missing its first digit! [Johnson]
The number n that starts the smallest chain of ten
consecutive hypotenuse
numbers n, n + 1, n + 2, ...,
n + 9 is an emirp. [Beedassy]
The most field goals in a professional basketball season is 1597 (Wilt Chamberlain, 1961-1962). [Homewood]
The smallest distinct-odd digit "extra" center-deletable prime (emirp), i.e., deleting the central double-digit prime, another prime remains. [Loungrides]
The internal digits of 1597 form 59 and outer digits form 17. Note that 59 is the 17th prime! [Palo]
(1597, 7951) is the 1st pair of 4-digit emirps consisting
of distinct odd digits. [Loungrides]
√(1597²*5)-4 is a Lucas prime. This is true for the four previous Fibonacci primes. [Homewood]
The word "essay" came into English in a 1597 work by Sir Francis Bacon. [Langley]
"The Merry Wives of Windsor" is a comedy by William Shakespeare believed to have been written in or before
1597. [Lou]
The "military compass" was designed and built by Galileo Galilei around 1597. [Boggs]
The prime number 1597 represents the initial obstinate
Fibonacci number in the sense that it is not expressible as
the sum of a prime and a power of two in at least one way
and serves as the first counterexample in this iconic
sequence to de Polignac's conjecture. [Schiffman]