MathDB

Consecutive interesting integers

Source: 43rd International Tournament of Towns, Senior O-Level P1, Fall 2021

February 18, 2023

number theoryprime numbersTournament of Towns

Problem Statement

Let us call a positive integer

k{}

interesting if the product of the first

k{}

primes is divisible by

k{}

. For example the product of the first two primes is

2\cdot3 = 6

, it is divisible by 2, hence 2 is an interesting integer. What is the maximal possible number of consecutive interesting integers?
Boris Frenkin