MathDB

The increasing sequence of natural numbers

a_1,a_2,\ldots

is such that for every

n>100

the number

a_n

is equal to the smallest natural number greater than

a_{n-1}

and not divisible by any of the numbers

a_1,\ldots,a_{n-1}

. Prove that there is only a finite number of composite numbers in such a sequence.
Proposed by P. Kozhevnikov

Problem Statement