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UKMT Cayley Olympiad, 2021

Number theory Difficulty 3.0 AMC 10/12 Prove it United Kingdom

In the four-digit number 4753, three two-digit numbers are formed by successive pairs of digits (47, 75, 53). Exactly two of these two-digit numbers are prime. Find all four-digit numbers in which all four digits are prime, and all three two-digit numbers formed by successive digits are prime.

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