Prime Time
Consider a digital clock. The first time after midnight when the three digits are all prime numbers is 2:22 am. What is the last time before 10:00 am when the three digits on the clock are all prime numbers?
Details and assumptions
If you determine that the time is 4:23 am, enter 423 as your numerical answer.
The answer is 757.
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1 solution
The single digit prime numbers are 2 , 3 , 5 , and 7 . Thus, the latest hour will be 7 am. Since there are 6 0 minutes in an hour, the tens digit cannot be 7. It follows that the tens digit is 5 . Finally, the largest possible units digit is 7. Hence, the last time is 7:57 am, so the answer is 757.