Number theoryDifficulty 5.0AIME, harderFind the answerUnited Kingdom
The number M=124563987 is the smallest number which uses all the non-zero digits once each and which has the property that none of the pairs of its consecutive digits makes a prime number. For example, the 5th and 6th digits of M make the number 63 which is not prime. N is the largest number which uses all the non-zero digits once each and which has the property that none of the pairs of its consecutive digits makes a prime number. What are the 5th and 6th digits of N?
(A) 6 and 3 (B) 5 and 4 (C) 5 and 2 (D) 4 and 8 (E) 3 and 5
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