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set of prime numbers

Source: VII May Olympiad (Olimpiada de Mayo) 2001 L1 P4

September 22, 2022
number theoryprime numbers

Problem Statement

Using only prime numbers, a set is formed with the following conditions: Any one-digit prime number can be in the set. For a prime number with more than one digit to be in the set, the number that results from deleting only the first digit and also the number that results from deleting only the last digit must be in the set. Write, of the sets that meet these conditions, the one with the greatest number of elements. Justify why there cannot be one with more elements.
Remember that the number 11 is not prime.