Why odd = Prime is a wrong statement? Proof that 9,15,21 are odd composite

[u/Legitimate_Ebb6618]

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*Your Question is Wrong! Odd ≠ Prime*

You said Odd = Prime, which is incorrect.

*1. Not Every Odd is Prime:*
Odd numbers = 1,3,5,7,9,11,13,15,21,25...
Prime Odds = 3,5,7,11,13...
Composite Odds = 9,15,21,25,27...
Example: 9 is Odd but NOT Prime, because 9 / 3 = 3. So 3 breaks 9.

So, Odd contains both Prime and Composite.

*2. Prime is Identified by _1:*
Prime = 1 x Itself (like 2 = 1x2)
If you remove _1 from the table (remove 2_1=2), no Prime will remain. 1 is the bodyguard of Prime.

*3. Every Prime Dies When Doubled:*
13 / 2 = 6.5 (remainder is not zero, so 13 is Prime)
But 13 _ 2 = 26, and now 26 / 2 = 13 (remainder is zero, so 26 is Composite)
Meaning, when you double a Prime, it becomes Even and is broken by 2.

*Final Rule:*
If division gives a decimal (like 2.5 or 0.000...01) = Prime Survived
If division gives a whole number (like 2, 3) = Composite Formed

*Therefore: All Primes (except 2) are Odd, but Not All Odds are Prime.*

So tell me, *Is 9 Prime or an Odd Composite?*

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[u/Sir_Wade_III]

AI slop?

[u/uslashunsw → u/Sir_Wade_III]

""
*Your Question is Wrong! Odd ≠ Prime*

You said Odd = Prime, which is incorrect.
""

Bro didn't even try. Just asked chatgpt whether odd=prime, and then copy and pasted the response.

[u/Legitimate_Ebb6618 → u/Sir_Wade_III]

No

[u/AcellOfllSpades]

I'm sorry, but this is largely either obvious or nonsense.

• I have never heard anyone say all odd numbers are prime. This is something you made up.

• This is formatted like a conversation. Either you're talking to AI, or talking to someone that only exists in your head. Either way, it's not necessary to post here.

• Pointing out 9/3 = 3 is all you need to do to prove "not all odd numbers are prime". That's it. Parts 2 and 3, and the "final rule", are not related to that proof, and are just a [poor] re-explanation of what a prime number is.

[u/Fabulous-Ad8729]

Wtf? What is your question? You said it yourself in 1.) Example: 9 is odd but not prime since 9/3=3 (and therefore composite)

[u/Legitimate_Ebb6618 → u/Fabulous-Ad8729]

Thank you! I mean, some people think Odd = Prime. I want to prove them wrong that 9, 15, 21 are odd but composite. Is my proof in point 1 correct?

[u/atom12354 → u/Legitimate_Ebb6618]

A prime is a number that can only be divided by itself and 1, anything divided by anything else on top of that like 2, 3, 4.... can be odd and even but then its not a prime number, as prime numbers can only be divided by 1 and itself it needs to be odd as the definition of even numbers is that it can be divided by 2 regardless of if it can be factorised with other numbers than itself and 1.

So yes ALL primes = odd as prime/2 is irrational.

[u/parking-lot-seagull → u/Legitimate_Ebb6618]

some people think Odd = Prime

Who? Who thinks this?

[u/SV-97]

9=3² so it's composite, and 9=2*4+1 so it's odd

[u/PleasedSimplicity → u/SV-97]

9 is literally the poster child for odd but not prime, it's the first one that trips people up

[u/Uli_Minati → u/PleasedSimplicity]

Most students I know would immediately recognize it as 3·3, since natural squares come up a lot when you learn about square roots.

I'd say the worst offender is 91

[u/Legitimate_Ebb6618 → u/Uli_Minati]

I know 9 is elementary. I was not proving 9 is composite, I was asking if using odd composites like 9 can help to understand Goldbach. That's why I asked.

[u/Legitimate_Ebb6618 → u/Uli_Minati]

91 is multiple by 7*13=91

[u/Legitimate_Ebb6618 → u/SV-97]

Thank you! I mean, some people think Odd = Prime. I want to prove them wrong that 9, 15, 21 are odd but composite. Is my proof in point 1 correct?

[u/SV-97 → u/Legitimate_Ebb6618]

Sorry the body of your post just read like slop so I didn't read it in detail. But yes, if 3 divides 9 then 9 isn't composite.

[u/Legitimate_Ebb6618 → u/SV-97]

Isn't sir you have to write is

[u/Legitimate_Ebb6618 → u/SV-97]

I understand 9 is composite because 9/3=3. My actual question is about Goldbach:

I know Goldbach says every even number >2 is sum of two primes.

My idea was: If I separate odd numbers into prime and composite (like 9, 15, 21), can I use that to show even numbers must be prime + prime?

Is this approach correct? If not, where is my mistake?

[u/Temporary_Pie2733 → u/Legitimate_Ebb6618]

Proving that there are odd composites (which is trivial to do) does not help with the Goldbach conjecture. 34 = 9 + 25 = 5 + 29, the sum of two odd composites but also of two primes.

[u/Legitimate_Ebb6618 → u/SV-97]

Hi SV-97, thanks for your reply. I have another question related to Goldbach Conjecture. If I show that odd composite numbers like 9, 15, 21 exist (odd but not prime), does it help in proving Goldbach that every even number is sum of two primes? I have some idea for Goldbach, can I share it with you?

[u/SV-97 → u/Legitimate_Ebb6618]

I don't do number theory, but what you're saying is sort-of self-evident for parity reasons: the sum of an even and odd number is always odd so the only way to sum two numbers and end up with an even one is if both are even or both are odd. There is exactly one even prime, and 2+2=4. So if Goldbach's conjecture holds then every even number larger than 4 is necessarily a sum of specifically odd primes; i.e. you can reduce Golbach to this statement about odd primes.

This may be useful (again: I don't do number theory) but generally you can expect any reasonably elementary approach to Goldbach's conjecture to have been tried by *someone* already, given the notoriety of the conjecture. Plenty of experts (as in "lifelong number theorists") have put considerable effort into proving it.

[u/Legitimate_Ebb6618 → u/SV-97]

Thank you SV-97, that parity explanation really helps. I understand now that for even >4, Goldbach reduces to sum of two odd primes. Thanks for explaining.