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:
∙ n is greater than all numbers on the already picked plums,
∙ 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 100000 a plum number?
Justify your answer. number theorycombinatorics