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# How to find the Nth prime number

Posted on 2007-11-28
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I need to find the Nth prime number. I.E. if the input is 3 it should return 5 because the first three prime numbers are 2,3, and 5. 4 should return 7 and so on. I just need an algorithm or some pseudocode here right now because i'm writing this in assembler. So far this is what i have.

for(divisor = 2; divisor < num; divis++)
{
if((num mod divisor) == 0)
num is not prime
break out of the loop
}
if((num - divisor) == 1)
num is a prime
//if num - divisor == 1 that means that it made it the whole way through the for loop without being broken out of the loop and there was no number that would divide the number therefore it is prime.

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Question by:toymachiner62
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LVL 6

Expert Comment

ID: 20371524
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LVL 6

Expert Comment

ID: 20371548
There is a site for calculating the n-th prime, and it explains a bit of the algorithm you may be interested
http://primes.utm.edu/nthprime/algorithm.php
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LVL 29

Expert Comment

ID: 20371817
I would recommend to have a look at wikipedia "Prime number" (http://en.wikipedia.org/wiki/Prime_number).  You will find there some theory and also a lot of references.

See the section "5.1 Finding prime numbers" (http://en.wikipedia.org/wiki/Prime_number#Finding_prime_numbers). The very first references in the section point to the "easy, brute force" and "fast" algorithms:

Sieve of Eratosthenes (http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes)
Sieve of Atkin (http://en.wikipedia.org/wiki/Sieve_of_Atkin -- contains reference to implementation in Python and in C)
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Accepted Solution

Talmash earned 750 total points
ID: 20372965
beyond the info on web:

find = 4 // find first 4 primes
found=1 // still only "2" found
print "2\n"
num = 3 // check if num is a prime

while (found < find) {
for(divisor = 2; divisor < num; divis++) {
if((num mod divisor) == 0) {
num is not prime
break out of the "for" loop
}

if(divisor*divisor > num) {
//if((num - divisor) == 1)
num is a prime
print num
found++
break out of the "for" loop
}
} // close "for"
} // close while

this code is closer to what you need.

tal
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