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2005-01-02, 17:15
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#1 |
Nov 2004
UK
2616 Posts |
Calculating sieving % accuracy
Is there a simple formula for determining what chance a positive integer N, will have of being prime after sieving out prime numbers up to sqrt(N)?
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2005-01-02, 19:02
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#2 | |
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Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2×3×29×67 Posts |
Quote:
If by "up to sqrt(N)" you mean "<= sqrt(N)", the probability of N being prime is unity --- it is a certainty because if N is composite, it has at least one prime factor <= sqrt(N). If you mean "< sqrt(N)", the only possible way in which it could be composite is if N=p*p, where p is prime. Given that this reasoning is so simple, I wonder if you meant to ask a different question? Paul |
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2005-01-02, 19:29
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#3 |
Jul 2004
Potsdam, Germany
3×277 Posts |
I had the same thought - it could be the case that the sqrt(N) in the question is meant for candidates, not for possible factors.
So the biggest possible factor tested would be sqrt(sqrt(N))... |
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2005-01-02, 19:34
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#4 |
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Nov 2004
UK
2616 Posts |
 My error folks - sorry for the darn silly question
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