Complexity of a simple algorithm to find a prime number

Question

I want know if the asymptotic complexity of this simple algorithm to find a prime number is O(n):

PrimeNumber(n)
Int i;
If (n%2=0) then { return "not prime"; }
Else {
  For(i=3;i<(√n)+1;i=i+2;){
    If (n%i=0) then {return "not prime";}
  }     
}
return "prime";

score 4 · Answer 1 · answered May 19 '17 at 14:11

4

Time complexity is O(sqrt(n)), since the loop iterates itself (sqrt(n)+1-3)/2 times, which is in O(sqrt(n)).

Note that since O(sqrt(n)) is a subset of O(n), it is also correct to say it is O(n) - but that bound is not tight.

answered May 19 '17 at 14:11

amit

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That's the complexity when the argument `n` is indeed prime. The complexity when `n` is composite requires some number theoretic analysis. – President James K. Polk May 25 '17 at 20:29
@JamesKPolk This is worst case complexity. – amit May 25 '17 at 20:30

Complexity of a simple algorithm to find a prime number

1 Answers1