Q:What are the largest and smallest 5-digit numbers that satisfy the following conditions?
1. Each digit of the number is a prime digit.
2. Each successive pair of digits forms a 2-digit number that is NOT a prime number.
3. Each of the prime digits must appear at least once in the 5-digit number.
A: Largest: 35772
Smallest: 32257
Definition of Prime Numbers from Coolmath.com
Prime digits are 2, 3, 5 and 7. 1 is not considered a prime number or digit.
Taken as pairs, the only combinations that satisfy condition 2 are:
22, 25, 27, 32, 33, 35, 52, 55, 57, 72, 75 and 77.
Of that list, 33 is the only number that contains a 3 as the second digit and so for condition 3 to be satisfied, 3 can only appear at the start of the 5-digit numbers.
Many thanks to Braingle
