Timeline for What is easier to find, the next prime number or next zero of zeta function?
Current License: CC BY-SA 4.0
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| Jan 22, 2023 at 11:17 | history | edited | Alex Peter | CC BY-SA 4.0 |
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| Jan 22, 2023 at 11:08 | history | edited | Alex Peter | CC BY-SA 4.0 |
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| Jan 22, 2023 at 11:00 | history | edited | Alex Peter | CC BY-SA 4.0 |
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| Jan 21, 2023 at 23:08 | comment | added | Zach Teitler | To find primes up to $n^2$ by Eratosthenes you need the primes up to $n$, not the first $n$ primes. | |
| Jan 21, 2023 at 21:53 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Jan 21, 2023 at 21:29 | history | edited | Alex Peter | CC BY-SA 4.0 |
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| Jan 21, 2023 at 21:25 | history | edited | Alex Peter | CC BY-SA 4.0 |
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| Jan 21, 2023 at 21:24 | history | edited | Alex Peter | CC BY-SA 4.0 |
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| S Jan 21, 2023 at 21:23 | review | First answers | |||
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| S Jan 21, 2023 at 21:23 | history | edited | Alex Peter | CC BY-SA 4.0 |
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| Jan 21, 2023 at 21:12 | comment | added | Alex Peter | @JoshuaZ Some, but essentially you do need quite some number of previous primes. You can say that you need first $n$ primes to decide up to $n^2$ primes, sure, but the essence is that you do need some number of first primes anyway. | |
| Jan 21, 2023 at 17:26 | comment | added | JoshuaZ | You still don't need all the prior primes to check what the next prime is. You'll have some interval where you can check each one's primality without checking all the primes before that value. | |
| Jan 21, 2023 at 17:00 | comment | added | Alex Peter | @JoshuaZ I compared Eratosthenes and calculating Riemann zeta zeros first. Then I am mentioning other algorithms for testing primes. The problem is that the question is asking about the next prime number, suggesting that you want to have all of them or at least some of them in some region first before deciding about the next. This is why testing prime number is simply different thing. | |
| Jan 21, 2023 at 16:40 | comment | added | JoshuaZ | "The difference is that you can find a very large Riemann zeros without knowing any previous zero, while you need to find all primes before any given value if you want to be 100% sure that you have found a prime number." This is not accurate. For example the AKS algorithm is completely deterministic and does not require knowing all the prior primes. This is not the only example. Many other procedures will give you a certificate of primality which can be easily checked without having all the prior primes. | |
| Jan 21, 2023 at 16:35 | review | Late answers | |||
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| S Jan 21, 2023 at 16:15 | review | First answers | |||
| Jan 21, 2023 at 17:07 | |||||
| S Jan 21, 2023 at 16:15 | history | answered | Alex Peter | CC BY-SA 4.0 |