# I'm a number with a special product, so name me when you think you've got it

In the blocks that come before,

their special product tells us more.

To guess my scheme you'll need calculation,

but only little tests of recreation.

Each block contains atoms strong as Thor,

which further join to make a score.

Yet some atoms die if they do not share,

no paths to find without a care.

What finally joins must have intersection,

in order to make my fine collection.

I'm a number with a special product,

so name me when you think you've got it.

Hint 1

from math import factorial from itertools import combinations

Hint 2

Make use of prime factors.

Hint 3

The factors of a factorial that are used to calculate the factorial can form a set.

Hint 4

The path weights represent the number of times that something is shared, with edges of weight 0 being dropped out of the graph altogether.

Hint 5

We might consider a subset of the Cartesian product of factors that are used to calculate a number.

• What do you exactly mean by Hint #3? The first hint is a python code and assuming that the third hint's 'set' is related to python meaning that it can only have unique elements, and since all numbers have unique prime factors but at various powers, what is the message conveyed by you exactly? @Galen Commented Jun 27, 2020 at 7:44
• Is the 5-7 connection correct? Commented Feb 1, 2021 at 21:28