If so, considering that multiples of the same numbers are always the same, and all numbers that are prime are indivisible, the only way the conjecture could be false is if there were indivisible numbers that aren't prime. Definition inconsistency.
That's why I'm not a mathematician.
https://en.wikipedia.org/wiki/Irreducible_element https://en.wikipedia.org/wiki/Prime_element
Trying to read that is like trying to learn an entire new language by reading a sentence in it. Way too many words to already understand what it's even defining (commutative ring, irreducible polynomials, UFDs, principle ideal, nozero prime ideal... and I'm not following why p divides ab in R... or even exactly what that means).
Searching youtube kahn academy and numberphile, but not turning up anything. exactly how high level is this?
Michael Artin's Algebra is a good, concrete book with tons of motivation and zero prerequisites. Wanna try it? ;)
I love it when my error is so simple that there isn't any question in my mind I missed something.
Edit: As pointed out elsewhere (and in the sibling to this comment) there are systems where "prime" and "irreducible" are not the same thing. In the integers they are, and that's sort-of why the FTA is true, but in other places they aren't, which is why the FTA is not obvious.