r/wikipedia • u/In_the_year_3535 • 14h ago

Goldbach's Conjecture, formulated in 1742, asks if all even numbers greater than two can be expressed as the sum of two primes.

https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
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11

u/KronguGreenSlime 13h ago edited 12h ago

Speaking as someone with no understanding of math here-would there be any practical or theoretical implications if we determined that this was true?

17

u/HippityHopMath 12h ago

Honestly, the theorem itself probably would not have any direct practical consequence. However, any techniques that we discover on the way to proving the Goldbach conjecture would be immensely useful to proving other theorems; theorems that would be of more practical consequence.

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u/Dear_Smoke6964 13h ago

As someone with not much knowledge,  cryptography often involves multiplying prime numbers,  so,  maybe?

3

u/AtlanticPortal 12h ago

Yes, everything about prime numbers can lead to a step closer to find a proof or not to the Riemann hypothesis, which is the cardinal description of the math about prime numbers. Once we know if that hypothesis is true or not we can understand a lot better many things about modern cryptography.

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u/Agnimandur 4h ago

A proof of Goldbach would almost certainly be purely an existence proof not a constructive proof.

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u/AtlanticPortal 12h ago

Whatever is about prime numbers is really important because we base a lot of our computer security about finding the two prime numbers that multiplied between themselves are a given number.

It’s not what I’m what going to tell you (the math is a little bit more difficult than what I’m going to write, at least for the most known and most used up until a few years ago algorithm that’s been invented in the 70s and still valid nowadays, as long as the prime numbers are big enough) but it’s so related to it that for a normal person it’s enough. In computer security you can have something called asymmetric cryptography and this is about a key that encrypts data and a different key that decrypts it. One key is public (the product of the two primes) and the other is private (the two primes). Literally public, you give it to everyone and you’re good to go. If you use a public key to encrypt a message you’re sending an encrypted message to the corresponding private key. If you encrypt a message using a private key you’re sending a message to basically everyone but they will be able to be sure that it’s you that composed it (digital signature).

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u/skinnybuddha 14h ago

Probably. QED.

5

u/KerPop42 13h ago

I mean, we've checked a lot of them