Well, it's not that the number is prime. There are many numbers which don't back up at the same time every day that aren't prime, like 25hrs or 22hrs. Numbers w

Well, it's not that the number is prime. There are many numbers which don't back up at the same time every day that aren't prime, like 25hrs or 22hrs. Numbers which are more complex fractions of a full day will take longer to repeat. Depending on a more exact statement of the goal, the best constant interval to avoid repeating parts of the day on nearby dates would be to multiply a day's length by the golden ratio; this would be about every 38.833 hours. Since the golden ratio is irrational, you'll technically never repeat the same time. But if I remember correctly, it's the best number to space out the times uniformly throughout the day and also distantly between nearby days.