1327
This number is a prime.
The prime whose difference to the next prime (1361) is such that the Cramer relation (pn+1 - pn)/log(pn)2 is the maximum for any prime greater than 113. [Ludovicus]
The number of named openings and variations listed in the second edition of The Oxford Companion to Chess by Hooper and Whyld.
If you relax the rules for bowling to allow any number of frames (not just ten), then the highest score you can have while having a prime score every frame, is 1327 (in the 59th frame). [Keith]
Your lowest chance of being born in a prime number year in the past millennium was to have been born in the 14th century (11 prime numbers, from 1301 to 1399, with a record gap between 1327 and 1361). [Tammet]
1327 is the first prime number such that there is more than one multiple of 16 between it and the next prime (1361). Surprisingly, there are 3 multiples of 16 between 1327 and 1361 (1328, 1344, and 1360). [Jacobs]
"The Name of the Rose" is a debut novel by Italian author Umberto Eco. It is a historical murder mystery set in an Italian monastery in the year 1️⃣3️⃣2️⃣7️⃣. [Lewicki]