Urgent: Prime Number Algorithm [C++/pseudocode]

[niv]

Anyone know how to generate all the primes less than n in a relatively quick fashion? If I were to use nested loops, I'll get points taken off for efficiency...I'm looking for a linear algorithm.

C++ code is welcomed, but pseudocode explanations are as well.

 

[niv]

I do have an algorithm, but take a look at these results:

C:\Dev-C++\SRC>16
Enter the limit for which odd psuedo and regular prime numbers
less than this number will be found: 30
         1                   3
         2                   5
         3                   7
         4                  11
         5                  13
         6                  17
         7                  19
         8                  23
         9                  29
Total comparisons: [b]1.26645e+07[/b]
Total resizes: 8

C:\Dev-C++\SRC>

 

[f1done]

Why not nested loops? If they're what I think they are (for x do [for x do ...]), they should run okay. I made one for PHP, which runs upward through the numbers (okay, starting from 4, I cheated with the first two), and then finds the denominator for the modulus by calculating every number less than the square root of the first number- if none of them are 0, then it's prime. It did 1-1000 in about 0.07 seconds (I'm using an old Celeron 400, so on the modern day computers it would probably run faster...). I did leave it to calculate all primes from 1 to one million, but it took something like 11 minutes (wonder what my web host would say if I uploaded that on their server LOL). Still, it ran a lot faster than my friend's Javascript version, which took about 15 seconds for 1-1000!