Prime Time

A digital clock shows the time as running hours from 1-12 and minutes from 0-59. At the specific morning time, both hour and minute numbers are different primes that do not share any common digit, and when the minute number is divided by an hour number, the remainder is an odd prime. Moreover, if we change the number of hours into number of minutes (e.g. 1 hour = 60 minutes) = X and let the minute number on the clock =Y, then both X+Y and X-Y are prime.

What time is this? (Suppose you think it's 3:59 A.M. Then enter 359 as your answer.)