This number is a prime.
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]