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is 1000 a quasi-prime ?

Source: 2019 Irish Mathematical Olympiad paper 1 p1

October 5, 2020

number theory

Problem Statement

Define the quasi-primes as follows.

\bullet

The first quasi-prime is

q_1 = 2

\bullet

For

n \ge 2

, the

n^{th}

quasi-prime

q_n

is the smallest integer greater than

q_{n_1}

and not of the form

q_iq_j

for some

1 \le i \le j \le n - 1

. Determine, with proof, whether or not

1000

is a quasi-prime.

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