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bio website Om
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O}=

Aug
4
awarded  Popular Question
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
awarded  Nice Question
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
comment 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
comment 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
comment 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
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accepted Proof formalization
Feb
25
asked Proof formalization
Feb
25
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Feb
24
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