MathDB

Johnny once saw plums hanging, like eggs so big and numbered according to the first natural numbers. He is the first to pick the plum with number

2

. After that, Jantje picks the plum each time with the smallest number

n

that satisfies the following two conditions:

\bullet

n

is greater than all numbers on the already picked plums,

\bullet

n

is not the product of two equal or different numbers on already picked plums. We call the numbers on the picked plums plum numbers. Is

100 000

a plum number? Justify your answer.

Problem Statement