Here are all the prime years of the last century and this century.
You can use this list to answer the question. 

1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999,
2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089,
2099.

There is no strategy except to check each year to see if it is prime. Of course
only odd years that don't end in 5 can be prime, but that property doesn't
guarantee that a year is prime.

Edwin