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max possible no of primes before first composite in a sequence of integers

Source: Mexican Mathematical Olympiad 2000 OMM P4

July 28, 2018
number theoryprimeInteger sequencemaximum

Problem Statement

Let aa and bb be positive integers not divisible by 55. A sequence of integers is constructed as follows: the first term is 55, and every consequent term is obtained by multiplying its precedent by aa and adding bb. (For example, if a=2a = 2 and b=4b = 4, the first three terms are 5,14,325,14,32.) What is the maximum possible number of primes that can occur before encoutering the first composite term?
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