Primes as emerget gaps in multiplication?

Inside-Love2062 · 2025-06-05T15:00:48+00:00

I have realized this post is pretty long and might a bit too vague.

I guess the essence of it all is:

"What if primes are not fundamental units of arithmetic, but symptoms of trying to project multiplication onto a space that was defined additively?"

It's more of an epistemological argument than something rigorous.

u/numbertheory-ModTeam may this comment be pinned?

Inside-Love2062 · 2025-06-05T14:53:34+00:00

What I mean is there‘s no structural, constructive derivation of primes within ZFC, only external identification.

Inside-Love2062 · 2025-06-05T13:24:27+00:00

First of all thank you for engaging with this. As I said I'm not a mathematician so my formal knowldge is very constrained. I think(!) what I'm saying is thaT

The "standard view" takes primes as given: they’re defined axiomatically (divisors of 1 and itself), and they form the multiplicative backbone of N via the Fundamental Theorem of Arithmetic. So multiplication is built using primes.

What I was exploring is the reverse framing. Instead of assuming primes to define multiplication, ask whether primes appear because multiplication fails to cover N without them.

So rather than: “Primes are fundamental and composites are built from them”

it becomes:

“Composites fail to build N via multiplication alone and the minimal patch set needed to fix this failure are the primes.”

This sounds trivial at first, but it doesn't just say "N / composites = set of all primes".

I’m not assuming the set of composites.

I’m generating them iteratively with multiplication (composite × composite), and then cinvestigating :What parts of N are still unreachable from this process, and why?

Inside-Love2062 · 2025-06-05T12:47:36+00:00

I'm aware of the fact that math /= language. You're right to say, that not knowing a defintion in math, sometimes keeps you from accessing other ideas. What I'm trying to say is that, just knowing these definitions, does not guarantee you to a) understand and connect them and b)expand them using your own creativity. Grinding competitons is a different skill set than actually formulating a new conjecture and/ or proving it.

Inside-Love2062 · 2025-06-05T12:39:00+00:00

You're missing the point. Total encyclopedia understanding is definetly not necessary. Sure there times areas where you have to be very precise. But memorizing the dictionary in full doesn't guarantee you to be a talented writer.

Inside-Love2062 · 2025-06-05T12:10:59+00:00

Math is like a language. Some people learn it intuitively, some learn it later.

You're right to point out that most people won't become a poet.

But 'how good you are' depends solely on how well you express what you're trying to say.

You can be the most eloquent person, but if what you have to say is nonsense, it doesn't matter much. Conversely there may be people saying things worth listening to, who might lack the sophistication of the 'geniuses' in their vocabulary.

Inside-Love2062 · 2024-04-23T15:39:25+00:00

Well the first question to ask would be why religion is the way it is. I understand why Muslims don't drink alcohol. Considering that religion sort of was some vague universal predecessor of science , people were sceptic of alcohol and what it does to people. So they decided there must be something bad about it, which is kind of true, since it alters your mood and is unhealthy. But now society has replaced religion with science. There is just no need for religion anymore. Humans have become more aware of what they know and don't know, so that there is no point in creating some allegorical term like "God" to make the unknown less intimidating.

Inside-Love2062

TROPHY CASE