# CFLib.org – Common Function Library Project

## GetPrimes(topInt)

##### Last updated July 31, 2004

Version: 3 | Requires: CF5 | Library: MathLib

Description:
Creates an array of all the prime numbers from 1 to the specified integer.

Return Values:
Returns an array.

Example:

``````<cfdump var="#getprimes(1000)#">
``````

Parameters:

Name Description Required
topInt The number to calculate primes for. Yes

Full UDF Source:

``````/**
* Creates an array of all the prime numbers from 1 to the specified integer.
*
* @param topInt      The number to calculate primes for. (Required)
* @return Returns an array.
* @author Steven Van Gemert (svg2@placs.net)
* @version 3, July 31, 2004
*/
function GetPrimes(topInt) {
var stepInt = 0;
var i = 0;
var primes = arraynew(1);
var di = 4; //Wheel factor.
var maxfactor = 0;
var thisnumberoffactors = 0;
var thismaxfactor = 0;
var isprime = "yes";

if(topInt is 1) return primes;
primes = 2;
if(topInt is 2) return primes;
primes = 3;
if(topInt LTE 4) return primes;

maxfactor = ceiling(sqr(topInt));
primes = getPrimes(maxfactor); //Recursion call. Find the primes for the square root of the passed number.

//Make the current maxfactor odd. We will use this as a starting point for checking for primes above the square root of this number.
maxfactor = maxfactor + 1 + (1 * (not ((maxfactor + 1) mod 2)));

//Now determine the appropriate wheel factor beginning value.
if(not (maxfactor mod 3)){
maxfactor = maxfactor + 2;
di = 4;
} else if(not ((maxfactor + 2) mod 3)){
di = 2;
}
else{
di = 4;
}

thisnumberoffactors = arraylen(primes);
for(stepInt=maxfactor; stepInt lte topInt; stepInt=stepInt+di) {
di = 6 - di; //Implement wheel factor. Every third odd number will be divisible by 3. Don't check it.

//This will be the limit to where we check for factors. There must be at least one factor less than the square root of the number.
thismaxfactor = sqr(stepInt);

isprime = "yes"; //Assume this number is prime.

for(i=1; i LTE thisnumberoffactors; i = i + 1){ //For each factor...
if(not (stepInt mod primes[i])){
isprime = "no"; //Indicate that this number is not prime.
break; //Break if we find a valid factor.
} else if(primes[i] GT thismaxfactor){ //If we have reached the square root.
break; //Stop processing...we have now validated this number as a prime.
}
}
if(isprime)ArrayAppend(primes,stepInt); //If this number is prime, then add it to the array of primes.
}

return primes;
}
``````

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