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Primes (lemmy.ml)
submitted 1 year ago by HiddenLayer5@lemmy.ml to c/memes@lemmy.ml
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[-] CompassRed@discuss.tchncs.de 53 points 1 year ago

2 may be the only even prime - that is it's the only prime divisible by 2 - but 3 is the only prime divisible by 3 and 5 is the only prime divisible by 5, so I fail to see how this is unique.

[-] Huschke@programming.dev 22 points 1 year ago* (last edited 1 year ago)

Exactly, "even" litterally means divisible by 2. We could easily come up with a term for divisible by 3 or 5. Maybe there even is one. So yeah 2 is nothing special.

[-] salty_mariner@lemmy.world 21 points 1 year ago

"Threven" has a nice ring to it now that I think of it.

[-] jwmgregory@lemmy.world 9 points 1 year ago
[-] PipedLinkBot@feddit.rocks 3 points 1 year ago

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[-] h3mlocke@lemm.ee 3 points 1 year ago* (last edited 1 year ago)
[-] EatBorekYouWreck@lemmy.world 42 points 1 year ago

Even vs odd numbers are not as important as we think they are. We could do the same to any other prime number. 2 is the only even prime (meaning it is divisible by 2) 3 is the only number divisible by 3. 5 is the only prime divisible by 5. When you think about the definition of prime numbers, this is a trivial conclusion.

Tldr: be mindful of your conventions.

[-] alvvayson@lemmy.world 13 points 1 year ago* (last edited 1 year ago)

Yes, but not really.

With 2, the natural numbers divide into equal halves. One of which we call odd and the other even. And we use this property a lot in math.

If you do it with 3, then one group is going to be a third and the other two thirds (ignore that both sets are infinite, you may assume a continuous finite subset of the natural numbers for this argument).

And this imbalance only gets worse with bigger primes.

So yes, 2 is special. It is the first and smallest prime and it is the number that primarily underlies concepts such as balance, symmetry, duplication and equality.

[-] EatBorekYouWreck@lemmy.world 8 points 1 year ago

But why would you divide the numbers to two sets? It is reasonable for when considering 2, but if you really want to generalize, for 3 you’d need to divide the numbers to three sets. One that divide by 3, one that has remainder of 1 and one that has remainder of 2. This way you have 3 symmetric sets of numbers and you can give them special names and find their special properties and assign importance to them. This can also be done for 5 with 5 symmetric sets, 7, 11, and any other prime number.

[-] Foofighter@discuss.tchncs.de 4 points 1 year ago

Not sure about how relevant this in reality, but when it comes to alternating series, this might be relevant. For example the Fourier series expansion of cosine and other trig function?

[-] EatBorekYouWreck@lemmy.world 3 points 1 year ago* (last edited 1 year ago)

But then it is more natural to use the complex version of the Fourier series, which has a neat symmetric notation

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[-] Severed_Fate@lemmy.world 40 points 1 year ago

2 is a prime though isn't it

[-] csfirecracker@lemmyf.uk 55 points 1 year ago

Yes, but it's the only even one. Making him the odd man out

[-] Gap@lemmy.world 39 points 1 year ago

It is but if feels wrong

[-] ipha@lemmy.world 2 points 1 year ago* (last edited 1 year ago)

It pretends to be prime and we all go along with it to avoid hurting its feeling.

[-] AssortedBiscuits@hexbear.net 27 points 1 year ago

The meme works better if it's 1 instead of 2. 1 is mostly not considered a prime number because a bunch of theorems like the fundamental theorem of arithmetic would have to be reworked to say "prime numbers greater than 1." However, just because 1 is not a prime number doesn't mean it's a composite number, so 1 is a number that is neither prime nor composite.

[-] Collatz_problem@hexbear.net 9 points 1 year ago

2 is a prime number, but shit ton of theorems only apply to odd prime numbers, and a lot of other theorems treat 2 as a special separate case, because it behaves weirdly.

[-] Whirlybird@aussie.zone 7 points 1 year ago

2 is a prime number though…..

Is it Just because it’s the only even one?

[-] JohnDClay@sh.itjust.works 7 points 1 year ago

Often things hold true for all primes except 2. You come across things like "for all non two primes"

[-] wischi@programming.dev 4 points 1 year ago* (last edited 1 year ago)

Any examples? Sounds like you mean the reason why one is excluded from the primes because of the fundamental theorem of arithmetic.

[-] kogasa@programming.dev 3 points 1 year ago* (last edited 1 year ago)

No, he's right. "For any odd prime" is a not-unheard-of expression. It is usually to rule out 2 as a trivial case which may need to be handled separately.

https://en.wikipedia.org/wiki/Fermat%27s_theorem_on_sums_of_two_squares

https://www.jstor.org/stable/2047029

https://www.jstor.org/stable/2374361

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[-] Whirlybird@aussie.zone 2 points 1 year ago

Like what? Genuine question, have never heard of this.

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[-] wischi@programming.dev 3 points 1 year ago

And how is "even" special? Two is the only prime that's divisible by two but three is also the only prime divisible by three.

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[-] EunieIsTheBus@feddit.de 7 points 1 year ago

Two is the oddest prime of them all.

[-] Aatube@kbin.social 7 points 1 year ago

I don't get it, why does adding a hand move to the next prime?

[-] MyFeetOwnMySoul@lemmy.ca 12 points 1 year ago

🚨 NERD ALERT🚨

Go define a vector space, nerd.

Go compute the p value of you being cool

Go integrate f(x)= 1/x on the domain (-1,1)

This is meme-ville population: me

Take a hike.

[-] MyFeetOwnMySoul@lemmy.ca 4 points 1 year ago

Spoiler: p < 0.05

[-] EatBorekYouWreck@lemmy.world 3 points 1 year ago* (last edited 1 year ago)
  • let V be you mom’s vagina, a vector space over the field of pubes. We define my d as a vector such that d is in V. Thus my dick is in your mom’s vagina.

  • In this vector space p values are not defined, but I can assure you that my pp is > 9000.

  • The integral of f(x)=1/x from -1 to 1 does not converge, just like how your father is never coming back from buying milk. The principal value of that integral tho is 0, just like the amount of hugs you got as a kid.

  • math is cool, you just too stupid to get it.

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[-] Aesthesiaphilia@kbin.social 5 points 1 year ago

Pretty sure that when we plug in a correction factor for the relative age of the Fediverse userbase, "today's lucky 10,000" becomes more like "today's lucky 10 million"

[-] Machefi@lemm.ee 2 points 1 year ago

Lucky ten thousand

I kinda wish it was calculated for the world instead of the US though

[-] HonoraryMancunian@lemmy.world 2 points 1 year ago

It's just the way the power rangers combined their forces

[-] WolfhoundRO@lemmy.world 7 points 1 year ago
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[-] NewEnglandRedshirt@lemmy.world 6 points 1 year ago

Oh yeah? What about 0? And 1?

[-] Chais@sh.itjust.works 36 points 1 year ago* (last edited 1 year ago)

They're not prime. By definition primes have two prime factors. 1 and the number itself. 1 is divisible only by 1. 0 has no prime factors.

[-] CAPSLOCKFTW@lemmy.ml 16 points 1 year ago

Commonly primes are defined as natural numbers greater than 1 that have only trivial divisors. Your definition kinda works, but 1 can be infinitely many prime factors since every number has 1^n with n ∈ ℕ as a prime factor. And your definition is kinda misleading when generalising primes.

[-] Chais@sh.itjust.works 9 points 1 year ago* (last edited 1 year ago)

Isn't 1^n just 1? As in not a new number. I'd argue that 1*1==1*1*1. They're not some subtly different ones. I agree that the concept of primes only becomes useful for natural numbers >1.
How is my definition misleading?

[-] CAPSLOCKFTW@lemmy.ml 3 points 1 year ago* (last edited 1 year ago)

It is no new number, though you can add infinitely many ones to the prime factorisation if you want to. In general we don't append 1 to the prime factorisation because it is trivial.

In commutative Algebra, a unitary commutative ring can have multiple units (in the multiplicative group of the reals only 1 is a unit, x*1=x, in this ring you have several "ones"). There are elemrnts in these rings which we call prime, because their prime factorisation only contains trivial prime factors, but of course all units of said ring are prime factors. Hence it is a bit quirky to define ordinary primes they way you did, it is not about the amount of prime factors, it is about their properties.

Edit: also important to know: (ℝ,×), the multiplicative goup of the reals, is a commutative, unitary ring, which happens to have only one unit, so our ordinary primes are a special case of the general prime elements.

[-] Chais@sh.itjust.works 3 points 1 year ago

Oof, I remember why I didn't study math 😅
But thanks for the explanation

[-] CAPSLOCKFTW@lemmy.ml 2 points 1 year ago

Yeah, higher math is a total brainfuck :D You're welcome.

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[-] bstix@feddit.dk 5 points 1 year ago

0 has all the factors. Itself and any other number.

[-] Blackmist@feddit.uk 4 points 1 year ago

Put them in a sieve of Eratosthenes and see what happens.

Spoiler, they aren't.

[-] lowleveldata@programming.dev 3 points 1 year ago
[-] teancom459@mastodon.sdf.org 18 points 1 year ago

@lowleveldata @HiddenLayer5

You asking why 9 wasn’t at the party?

It’s because he’s a square

[-] Gap@lemmy.world 9 points 1 year ago
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this post was submitted on 09 Aug 2023
668 points (95.0% liked)

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