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A comment on Show HN: New world record – verified Goldbach Conjecture up to 4*10^18+7*10^13. Parent comment

Re:Show HN: New world record – verified Goldbach Conjecture ... by jay_gridbach on Saturday April 19, 2025 @04:24AM (#43735037)
All I can tell here is that I do certain level of valication on server side. As one of the goals of this project is to popularize the fun of mathematics among the general public, I think I would need to avoid a open network configuration to strictly conduct academic verification. The algorithm itself is publicly opened, so anyone can verify the computation step is correct or not. https://github.com/nakatahr/gridbach-core
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Re:Show HN: New world record – verified Goldbach Conjecture ... by comboy on Saturday April 19, 2025 @04:42AM (#43735108)
zk-SNARKS maybe?
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Re:Show HN: New world record – verified Goldbach Conjecture ... by Sesse__ on Saturday April 19, 2025 @05:29AM (#43735268)
For demonstrating verification of a conjecture, surely you can do much simpler things than a zero-knowledge proof: Send one of the primes.
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Re:Show HN: New world record – verified Goldbach Conjecture ... by sebzim4500 on Saturday April 19, 2025 @08:42AM (#43736025)
It would still take a nontrivial amount of computation to do all the verification afterwards. Back of the envelope calculations suggest it should less than 100x longer to find the two primes than to verify them.
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Re:Show HN: New world record – verified Goldbach Conjecture ... by yujzgzc on Saturday April 19, 2025 @01:45PM (#43738032)
It'd be neat to do the verification in the same manner by redistributing one client's results to another, therefore obtaining a proof modulo client collusion.
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Re:Show HN: New world record – verified Goldbach Conjecture ... by johnisgood on Saturday April 19, 2025 @10:46AM (#43736763)
I am curious about alternatives or solutions in such a setting / context.
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Re:Show HN: New world record – verified Goldbach Conjecture ... by looofooo0 on Saturday April 19, 2025 @11:37AM (#43737135)
Say smaller prime is less then 10,000. Then this one or two Byte per Nummer. E.g. 100 Mio number is already 100mb or
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Re:Show HN: New world record – verified Goldbach Conjecture ... by gus_massa on Saturday April 19, 2025 @09:44PM (#43740936)
Never trust the client. You must do a full verification. IIUC from another comment, you only ask the client to return the interval they tested and some token to ensure the server send them that interval.

You must ask for each number in the interval the two primes and a Primality certificate for each prime. https://en.wikipedia.org/wiki/Primality_certificate

The idea is that it's very hard to find the two primes and it's very hard to prove that they are actually primes. But if the client send you both primes and send you each primality certificate, then the verification is very fast. Also, you can store that info so people can see it.

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Re:Show HN: New world record – verified Goldbach Conjecture ... by jay_gridbach on Sunday April 20, 2025 @07:23PM (#43747281)
Thanks. Your advice is really helpful.
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