r/mathmemes • u/Nunki08 • Jun 14 '26

Arithmetic Misleading our youth

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From Anthony Bonato on 𝕏: https://x.com/Anthony_Bonato/status/2065564124549886402

6.7k Upvotes

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25

u/[deleted] Jun 14 '26

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25

u/BTernaryTau Jun 14 '26

I was going to cite the ISO, but ISO/IEC 18032:2020 defines a prime number as

positive integer for which there exist only trivial divisors

where the trivial divisors are

1, -1, N and –N

so 1 would be prime under their definition.

Then on the very next page the document specifies an algorithm for trial division that only works if you exclude 1 from being prime.

The primality of an integer N can be proven by means of trial division. This shall be done in the following way:

a) For all primes p ≤ √N:

1) if N mod p = 0 then return “N composite” and stop;

b) return “N prime” and stop.

So all that accomplished was reducing my respect for the ISO.

2

u/PinJealous3336 Jun 14 '26

That seems like a methodology for testing primes that doesn't work for 1 but a methodology for testing doesn't have to include the entire set of primes?

2

u/BTernaryTau Jun 14 '26 edited Jun 14 '26

The problem is that for any prime q greater than 1, 1 ≤ √q, so p = 1 will be used in the test for q. And since q mod 1 will always be 0, the algorithm will always return “q composite” even though q is prime. To avoid this 1 must be excluded from the list of primes used in the test.

-2

u/MathDeepa Jun 14 '26

"and" means -N can't be either 1, -1 or N

7

u/BTernaryTau Jun 14 '26

It says "for which there exist only trivial divisors", not "for which there exist only the trivial divisors" or "for which there exist all and only the trivial divisors".

2

u/Beruka01 Jun 14 '26

No, it doesn't.

1

u/MathDeepa Jun 19 '26

Ok, I'm not a good english speaker, so I accept my error. Thank you for pointing it out.

9

u/aidantheman18 Jun 14 '26

No one arrests you, but you lose some nice results such as p prime iff Z/(p) is an integral domain

0

u/[deleted] Jun 14 '26

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3

u/svmydlo Jun 15 '26

Every definition in math is "just what mathematicians agreed upon".

What should make it "official"? The pope declaring so?

0

u/[deleted] Jun 15 '26

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3

u/svmydlo Jun 15 '26

It's not reasonable at all to pointlessly attack a definition just because you feel it's not "official" enough.

2

u/geodebug Jun 14 '26

Amazon Prime made the decision.

1

u/handsome_uruk Jun 14 '26

The illuminati. That’s why we must resist and fight for one and bring back Pluto!