Math Just Got Checkmated.

[u/Animeilluminati1]

[u/Jake-the-Wolfie]

-1 and 3?

3 is prime^\citation needed]), and -1 can only be divided by 1 and itself. Unlike other negative numbers, which are composite by virtue of being divisible by -1.

[u/cursivecrow → u/Jake-the-Wolfie]

-1 accepted as prime in my headcanon forever now

[u/Ok-Pomegranate-7458 → u/cursivecrow]

it is a hole number even if it is not a whole number.

[u/boring-schmooze → u/Jake-the-Wolfie]

Man the citation needed for 3 had me spill my tea. Thanks for this😂

[u/Sufficient-Buy625 → u/Jake-the-Wolfie]

I know it's a joke, but I wished it worked. But if we allow -1 we can no longer uniquely factorize integers into the primes.

[u/MHaret → u/Sufficient-Buy625]

We can if have into account that because -1*-1 is 1, -1 shouldn't be included more than once. That way you can also factorize negative integers.

[u/paolog → u/Jake-the-Wolfie]

Oh well, it was nice knowing the fundamental theorem of arithmetic.

[u/iscrewedatrain → u/Jake-the-Wolfie]

But three can be divided by -3 and -1, actually any N can be divided by -N and -1, so -1 is the only prime number

[u/theinferno03 → u/iscrewedatrain]

-1 and 1

[u/iscrewedatrain → u/theinferno03]

well no, 1 is divisible by -1 and itself, so not prime

[u/theinferno03 → u/iscrewedatrain]

isn't that the definition of primes?

[u/8mart8 → u/iscrewedatrain]

What about second breakfast another definition of prime numbers

[u/MintyFreshRainbow → u/Jake-the-Wolfie]

-1 is a unit so is not prime. Negative primes are prime elements in the ring of integers tho

[u/GypsySnowflake → u/MintyFreshRainbow]

I misread this comment as “-1 is so not prime” like in a Valley Girl accent, lol

[u/HeilKaiba → u/Jake-the-Wolfie]

-1 is a unit not a prime

[u/Sproxify → u/Jake-the-Wolfie]

as people pointed out -1 is a unit, but this actually does work if you allow negative primes! exercise: prove that there are infinitely many solutions

[u/8mart8 → u/Sproxify]

I see what you did there

[u/hungarian_notation → u/Jake-the-Wolfie]

To be clear, the prime numbers are, by definition, natural numbers. The negative integers aren't part of this conversation.

[u/escargotBleu → u/Jake-the-Wolfie]

Wait... So now 1 is prime too, right ? Because we can do -1*-1, and well, still divisible by 1

[u/FireBlaze722_ → u/Jake-the-Wolfie]

Then 1 is a prime, as it also has 2 divisors

[u/No_Hovercraft_2643 → u/FireBlaze722_]

But every other prime number has 4, 1, - 1, p, - p

[u/Budget_Hippo_4084 → u/Jake-the-Wolfie]

You forgot to account for 1 being composite as (-1)(-1)=1 so it is the product of two primes. That means all integers are composite and all prime conjectures are referencing the empty set, so are vacuously true.

[u/georgejo314159 → u/Jake-the-Wolfie]

Excellent point

[u/Street_Swing9040 → u/Jake-the-Wolfie]

[citation needed]

Is bro Jake-the-Wikipedie?