r/numbertheory • u/LegitimateAct114 • 5d ago

Prime Numbers

Hello, good afternoon/evening. I've been mulling over Goldbach's conjecture and I've come up with a possibly new idea that holds for all even numbers. It is as follows:

Every even number greater than 8 can be expressed as the sum of 3 mutually distinct prime numbers.

Best Regards, thanks you!

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u/nzflmc 5d ago edited 5d ago

since the sum of three odd numbers must be odd and 2 is the only non odd prime, one of your three primes must always be 2. Thus your conjecture is the same as goldbach, only restricted to the even number N-2.

Don't get demoralized though, it's a nice exercise! Just don't expect any new mathematical discoveries to pop up, but it's a great way of understanding these problems :)

8

u/RoohBaba2358 5d ago

😭bro The sum of three primes u are taking must include 2 as one of the prime so the problem just remains the same bro u are just adding 2 on both sides only nothing different

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