Rampaging Primes

Logic Level 4

\(M\) is the largest \(5\)-digit number and \(N\) is the smallest \(5\)-digit number that satisfies the following conditions ---

  • Each digit of the numbers is a prime digit

  • Each successive pairs of digits forms a \(2\)-digit number that is NOT a prime number

  • Each of the prime digits must appear at least once in each of the \(5\)-digit numbers

Find \(M-N\)


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