This number is a prime.
According to the 16th century prophet Nostradamus, the Earth will survive until A.D. 3797. [Skinner]
3797 is the only four-digit prime, in which: i.The first digit and the last digit are primes (3,7). ii.The first two-digit number, the second two-digit number and the third two-digit number are primes (37,79,97). iii.The first and the last three-digit numbers are primes (379,797). [Sreechakra]
The center of a 7-by-7 magic square of primes which stays a magic square (but with 7 primes) if the units digits of all entries are removed (i.e., 9341 becomes 934, ...). [Madachy]
(3797, 3803, 3821) is the only occurrence of three successive primes p < 10000, such that the form 4*p+5 creates primes, i.e., 15193, 15217, 15289. [Loungrides]