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]

(There is one curio for this number that has not yet been approved by an editor.)

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