I saw a thread in the Java section about sexy primes and was intrigued, I had never heard of them. Although I've seen some very attractive primes in my time though, believe you me.


For a quick crash course in its definition, hit up the wiki page:

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I used a simple prime checker function. Feel free to use a more efficient/better/complicated one. Whatever floats your boat really.

//rather naive, feel free to use a sieve or whatever 
bool isPrime(int num){
	for(int i = 2; i <= sqrt((double)num); i++){if((num%i == 0)&& (num != i))return false;}
	return true;
}

All we need to do for a sexy prime is go from start to end (user defined or hard code, again up to you) checking prime-ness. Every time we hit a prime, we check 6 numbers ahead. If it's also prime, print:

void sexyPrimes(int start, int end){
	cout << "\n\nSexy Primes between " <<  start << " and " << end << endl;
	if (start < 2){ start = 2; }
	for(int i = start; i < end; i++){
		if(isPrime(i)){ //both must be prime
			if(isPrime(i+6)){
				cout << "{" << i << "," << i+6 << "}" << " "; //nice pair formatted output
			}
		}
	}
}

Easy no? Let's try a sexy triplet. To qualify as a sexy triplet:

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So the first part is the same as the sexy prime, except now we have to check i+12 after we verify i+6. THEN i+18 has to be not prime (composite):

void sexyTriplets(int start, int end){
	cout << "\n\nSexy Triplets between " <<  start << " and " << end << endl;
	if (start < 2){ start = 2;}
	for(int i = start; i < end; i++){
		if(isPrime(i)){
			if(isPrime(i+6)){
				if(isPrime(i+12)){
					if(!isPrime(i+18)){ //p+18 must be composite
						cout << "{" << i << "," << i+6 << "," << i+12 << "}" << " ";
					}
				}
			}
		}
	}
}

Tired of all the sexy numbers yet? No? Good. The next variation is a sexy quadruplet. It's criteria:

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So same deal as the triplet, except i+18 must now be a prime and the first number in the sequence ('i') must have a 1 in the ones place:

void sexyQuadruplets(int start, int end){
	cout << "\n\nSexy Quadruplets between " <<  start << " and " << end << endl;
	if (start < 2){ start = 2;}
	for(int i = start; i < end; i++){
		if(isPrime(i)){
			if(isPrime(i+6)){
				if(isPrime(i+12)){
					if(isPrime(i+18)){ //p+18 must be prime
						if((i % 10 == 1) || (i == 5)){
							cout << "{" << i << "," << i+6 << "," << i+12 << "," << i+18 << "}" << " ";
						}
					}
				}
			}
		}
	}
}

Sample implementation:

#include <cmath>
#include <iostream>
using namespace std;

//rather naive, feel free to use a sieve or whatever 
bool isPrime(int num){
	for(int i = 2; i <= sqrt((double)num); i++){if((num%i == 0)&& (num != i))return false;}
	return true;
}

void sexyPrimes(int start, int end){
	cout << "\n\nSexy Primes between " <<  start << " and " << end << endl;
	if (start < 2){ start = 2; }
	for(int i = start; i < end; i++){
		if(isPrime(i)){ //both must be prime
			if(isPrime(i+6)){
				cout << "{" << i << "," << i+6 << "}" << " "; //nice pair formatted output
			}
		}
	}
}

void sexyTriplets(int start, int end){
	cout << "\n\nSexy Triplets between " <<  start << " and " << end << endl;
	if (start < 2){ start = 2;}
	for(int i = start; i < end; i++){
		if(isPrime(i)){
			if(isPrime(i+6)){
				if(isPrime(i+12)){
					if(!isPrime(i+18)){ //p+18 must be composite
						cout << "{" << i << "," << i+6 << "," << i+12 << "}" << " ";
					}
				}
			}
		}
	}
}

void sexyQuadruplets(int start, int end){
	cout << "\n\nSexy Quadruplets between " <<  start << " and " << end << endl;
	if (start < 2){ start = 2;}
	for(int i = start; i < end; i++){
		if(isPrime(i)){
			if(isPrime(i+6)){
				if(isPrime(i+12)){
					if(isPrime(i+18)){ //p+18 must be prime
						if((i % 10 == 1) || (i == 5)){
							cout << "{" << i << "," << i+6 << "," << i+12 << "," << i+18 << "}" << " ";
						}
					}
				}
			}
		}
	}
}

//sample implementation
int main(){
	sexyPrimes(0,500);
	sexyTriplets(0,1000);
	sexyQuadruplets(0, 1000);
	return 0;
}

Output:

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I did modify it a bit so that groupings broken over my small console window were more readable. Neat huh?

Tell your friends, this is a very sexy blog.