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Jan
28 |
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Aug
4 |
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Jun
16 |
revised |
Sieve of Eratosthenes - eventual independence from initial values
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Jun
16 |
comment |
Sieve of Eratosthenes - eventual independence from initial values
I accepted this question as a 'no' to "Is this already known ? " and 'no' also to "Are there any known implications ?", which seem to reflect the other answers' and comments' insights as well. |
Jun
15 |
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Jun
15 |
revised |
Sieve of Eratosthenes - eventual independence from initial values
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Jun
15 |
accepted | Sieve of Eratosthenes - eventual independence from initial values |
Jun
14 |
comment |
Sieve of Eratosthenes - eventual independence from initial values
Thanks Theo, your reasoning is a lot cleaner than the one I had to prove my square-of-the-highest thing. I'll have a look at the thesis you link. I came to this result by thinking the primes in terms of rolling wheels ; each prime has its own wheel doing cycles and each time there is no wheel arriving to the end of its cycle, add a new wheel with cycle equal to the number of the iteration. Primes are really funny things. Thanks a bunch for your time ! |
Jun
14 |
revised |
Sieve of Eratosthenes - eventual independence from initial values
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Jun
14 |
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Sieve of Eratosthenes - eventual independence from initial values
No, after some number, all the primes are exactly the sames than the natural ones, and this number is computable. I did compute how long it takes to have a match, I think it was under the squared highest of the seed set, but I'm not sure and have not my notes right here. It would be computationally silly, though, I admit completely ! |
Jun
14 |
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Sieve of Eratosthenes - eventual independence from initial values
Hi Noldorin. Indeed if you take 4 and 5 as you initial primes, 6 and 7 will be counted primes, and 9 too. But eventually (I believe at most at the square of your highest seed-prime, here 25), you will get all the "natural" primes again. The 6, 7, 9 "false positives" are part of the recalibrating phase I talked about. |
Jun
14 |
comment |
Sieve of Eratosthenes - eventual independence from initial values
@Wadim : Sorry, for me the fact that prime numbers are independent from their predecessors, given a certain way to generate them, was not so obvious. :) I don't know either what kind of implications to get, that's why I asked. :) @Charles : Thanks. |
Jun
14 |
revised |
Sieve of Eratosthenes - eventual independence from initial values
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Jun
14 |
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Sieve of Eratosthenes - eventual independence from initial values
Nope let's say 8 is counted as a prime, then 16 is not anymore (twice 8). Then all the other powers of two are expressible as a certain number of 8's. |
Jun
14 |
awarded | Editor |
Jun
14 |
revised |
Sieve of Eratosthenes - eventual independence from initial values
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Jun
14 |
asked | Sieve of Eratosthenes - eventual independence from initial values |
Mar
8 |
accepted | Proof formalization |
Feb
25 |
asked | Proof formalization |
Feb
25 |
awarded | Supporter |