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"2 is the oddest prime" is a clever math quip. This would be the natural extension of that joke.

Expected we're gonna correct me by stating I should have written "throdderest", or something (can't recall your lingo).

In a threeven/throdd/throdder world, I assume we'd say things like, "isn't that throdd" or "that's so throdder", depending on degree

Daniel Wigton 3mo ago

Ahh! I am incapable of such cleverness. But really the only reason they are thinking of two being odd as a prime is the fact that it is the only even prime. Again caught in the trap of thinking divisibility by two is special somehow.

The one that bugs me is 1. It follows the rules of primes, only divisible by itself and one, but it is also in the definition excluding it from prime factorizations.

Why don't we have higher concepts like "only divisible by itself one and two."?

Or would it be more natural to say "only divisible by itself, one, or two."?

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Discussion

YODL 3mo ago

The definition does feel artificial on the edge case exclusion, but obviously for uniqueness it's necessary...

Kinda interesting why we don't have higher level concepts, as you say. Guessing you had this thought while toiling over the twin prime question.

Currently vibing on Surreal Numbers. A proper class, like the ordinals, but a generalization of all linear orders (instead of well orderings). Worth a gander if you're ever bored

Daniel Wigton 3mo ago

I took a look. But it was brief and kind of went over my head. It was hard to see how it was useful since you always have to construct the sets from the beginning.

YODL 3mo ago

The process of constructing them is fun to think about (transfinite recursion). For example, through the stages 0,1,2,etc we have a copy of the dyadic rational numbers (of form +/-m/2^n), but on first infinite stage, we get the reals, infinitesimals, and more). This chart is cool to visualize a bit, and all field operations are well defined (addition, division...)

nostr:nevent1qqsd2ynku78jhhj060t3xu3cptrve0f2c6rqj8gp8a3ree0xe4fecygpndmhxue69uhkummn9ekx7mp0y5erqamnwvaz7tmwdaehgu3wd3skuep0y5erqffjxpshvct5v9ez2v3swaehxw309ahx7um5wgh8w6twv5hj2v3sy5erqctkv96xzu39xgc8wumn8ghj7ur4wfcxcetjv4kxz7fwvdhk6te9xgc8wumn8ghj7un9d3shjtnyv9kh2uewd9hj7ffjxpmhxue69uhhyetvv9ujuumwdae8gtnnda3kjctv9ua60u6d

Daniel Wigton 3mo ago

I should upload my silly little twin primes paper for your enjoyment sometime. The trouble is that I wrote it in 2001 in Microsoft Works. I need to get it into LaTeX. Maybe AI can do that for me.

Daniel Wigton 3mo ago

The final result.

YODL 3mo ago

AWS and my wallet arent happy right now, or id zap preemptively. Will have a look, though I fear without the prior pages the notation may overwhelm me

Daniel Wigton 3mo ago

Yeah. Only the result matters. It is a simple formula. It just counts the number of twin elements of the Nth wheel sieve modulo it's length. A better treatment on wheel sieves can be found in Paul Pritchard's original paper. I just didn't know about it when I wrote mine.

YODL 3mo ago

I recall you mentioning him I think. The newton to your Leibniz

Daniel Wigton 3mo ago

Only I am not bitter about it. ... much. Ok not really at all. It would have been nice if my advisor had worked with me to publish the part that was unique. But we were a small school that didn't really think about publishing, especially for undergrad thesis papers which were usually just a report on some self-taught topic, not original work. There was no graduate department.

YODL 3mo ago

Skimming it I see what it's saying I think. Funny way to lay out induction, sorta backwards and no explicit mention of "induction" in proof.

Very cool to put all of this together though, at such a young age no less 👑

Daniel Wigton 3mo ago

I was and still am, very bad at writing proofs.

Daniel Wigton 3mo ago

It isn't induction exactly. The proof works without it, but to get the right initial index I picked a set whose order I could easily count as the starting point.

At least I think that's how it went.

YODL 3mo ago

I only gave a short look after Wikipedia skim of what the sieves were, so maybe missed something. Will come back to it when my fiat overlords aren't suppressing my curiosity of things outside spreadsheets 🥲

YODL 3mo ago

Looked again and still seems like induction to me, but I'll take your word for it since there are too many symbols I'm only vaguely guessing at from context. Number theory hurts my brain

Daniel Wigton 3mo ago

You are probably right. Like I said. I am bad at proofs. I do like some number theory though. I'll have to dig into those fantasy numbers at some point. They may have some tricks I could use.

Daniel Wigton 3mo ago

Lol, sorry, surreal numbers.

YODL 3mo ago

They're not entirely useless. But I doubt you'll find any application. It really is kinda cool to try to grasp them, and it's a shame they're omitted from early curriculums