largest primary divisor number
Source: Dutch NMO 2022 p1
November 17, 2022
number theorydivisor
Problem Statement
A positive integer n is called primary divisor if for every positive divisor of at least one of the numbers and is prime. For example, is divisor primary, because its positive divisors , , , and each differ by from a prime number (, , , and , respectively), while is not divisor primary, because the divisor does not differ by from a prime number (both and are composite). Determine the largest primary divisor number.