This number is a prime.
The number of ones that form the fourth repunit prime. It was first proven prime by Hugh C. Williams in 1977. [Dobb]
Romanian mathematician Dimitrie Pompeiu (1873-1954) posed the following puzzle: ABC398246 is a nine-digit number exactly divisible by 317, whose first three digits (A,B,C) are unknown. What are the digits A, B, and C?
"317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way." (G. H. Hardy, A Mathematician's Apology, 1940)
The sum of the squares of the digits of the prime 317 is 59, another prime. Note that all odd digits are present. [Trotter]
317 = (-3)3 + 13 + 73. [Dobb]
317# - 1 is a primorial prime. [Dobb]
A door with room number 317 appears in film footage taken of Lee Harvey Oswald shortly before his death.
The giant statue of Buddha in the lamasery of Yung-Ling, China, doubles as an object of veneration and a library containing 317 volumes of Tibetan classics. [Dobb]
Yasutoshi Kohmoto currently holds the record for the largest known unitary amicable pair, each member of which has 317 digits.
Former pitching ace Walter "Big Train" Johnson once hurled a coin 317 feet across the Rappahannock River in Virginia.
According to the Australian Bureau of Meteorology's Annual Climate Summary, 317 millimetres is the average annual rainfall over Australia for Australia's driest year since 1890 (1902).
Richard McIntosh notes that the largest prime of the form (2^4p + 1)/17 has p = 317, but that (2^4p + 1)/17 is composite for all prime p with 317 < p < 10000. Nobody knows if there are any more such primes. [Post]
The artist Norman Rockwell painted 317 covers for "Saturday Evening Post" magazine. [Dobb]
The smaller of only two 3-digit primes p such that 2^p+p is prime. The other is 701. [Loungrides]
The upperbound for Skewes's number has been improved by Patrick Demichel to 317 digits.
There are currently 317 recognized species of turtles and tortoises in the world. [Buhlmann]
After 1 and 2, n=317 is the smallest case in which n divides the prime index (6974) of the nth Honaker prime (70379). [Gaydos]
It is not known whether π(x) is ever greater than li(x) for any number less than 317 digits, assuming the Riemann hypothesis. [Zegowitz]
317 of the first thousand prime numbers have no digits in common with their prime indices. [Gaydos]
The smallest prime which is the sum of three consecutive sphenic numbers, i.e., 102 + 105 + 110. Note that 102 = 2 × [3*17]. [Worrom]