Military time is based upon a 24-hour clock. The time is expressed in the form abcd hours where a, b, c, and d are base 10 digits, ab is the hours, ranging from 00 to 24, and cd is the minutes, ranging from 00 to 59. (0000 and 2400 hours are equivalent, but one minute past midnight is still represented as 0001).
From his unit, Buck Private Kilroy was assigned to K.P. where he reported to duty on the hour. After a quick, but complete, demonstration on how to peel a potato by the mess sergeant, Kilroy was ordered to peel two potatoes every minute from abcd hours until efgh hours.
Upon timely completion of the task, the buck private was put to work in other kitchen duties for the remainder of the detail (where he could contemplate the meaning of "hurry up and wait") while waiting for the other members of his company to be called to chow hall at (hgfe + abcd) hours.
The following is known:
(a) The times, abcd, efgh, and (hgfe + abcd), are prime numbers;
(b) Each two digit hour and minute of efgh and (hgfe + abcd) are also prime numbers; and,
(c) The sum of the digits of abcd is divisible by three.
(d) Normal addition rules apply in adding the numbers representing "time" values. If a sum results in a value that is not in the form of a valid time, it obviously does not qualify as a solution.
According to the information given in the problem above, answer the following:
(1) What hour did Kilroy finish peeling potatoes?
(2) Given that the number is prime, how many potatoes were peeled?
(3) And, what time was the company of soldiers called to mess?