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jmc

number theory intermediate

Problem

Base prime representation of a natural number is defined using the exponents of its prime factorization as follows. Each place in a base prime represents a prime number, and it is occupied by the corresponding exponent of that prime, starting on the right side with the smallest prime number and proceeding to the left with the next largest prime number. For instance, since , then would be written as in base prime. What is written in base prime?
Solution
The prime factorization of is . Since does not divide into , we treat as having a exponent; the next two primes are and . Thus, the answer is
Final answer
220