(I) Assuming a lifespan of 80 years, in what years of the 20th and 21st centuries (1900-1999), (2000-2099) would you have to be born to have the maximum number of prime birthdays in a year whose sum of the digits is a prime number?

(II) In what years of the same time spans would you have to be born to have the minimum number of prime birthdays in a year whose sum of the digits is a prime number?

(For example, the sum of the digits of the year 1967 is 23, which is a prime number. People born in 1954 were 13 in 1967, which is also a prime number.)

Note: For the purposes of the problem, assume that that people born on Feb. 29 in a leap year still celebrate their birthdays each following year.