MathDB

Let

s(n)

denote the smallest prime divisor and

d(n)

denote the number of positive divisors of a positive integer

n>1

. Is it possible to choose

2023

positive integers

a_{1},a_{2},...,a_{2023}

with

a_{1}<a_{2}-1<...<a_{2023}-2022

such that for all

k=1,...,2022

we have

d(a_{k+1}-a_{k}-1)>2023^{k}

and

s(a_{k+1}-a_{k}) > 2023^{k}

?
Proposed by Nikola Velov

Problem Statement