A Pierpont prime is a prime number of the form: 2u3v + 1 for some non-negative integers  u  and  v .



A Pierpont prime of the second kind is a prime number of the form: 2u3v - 1 for some non-negative integers  u  and  v .


The term "Pierpont primes" is generally understood to mean the first definition, but will be called "Pierpont primes of the first kind" on this page to distinguish them.



Task

 Write a routine (function, procedure, whatever) to find Pierpont primes of the first & second kinds.
 Use the routine to find and display here, on this page, the first 50 Pierpont primes of the first kind.
 Use the routine to find and display here, on this page, the first 50 Pierpont primes of the second kind
 If your language supports large integers, find and display here, on this page, the 250th Pierpont prime of the first kind and the 250th Pierpont prime of the second kind.


See also

 Wikipedia - Pierpont primes
 OEIS:A005109 - Class 1 -, or Pierpont primes
 OEIS:A005105 - Class 1 +, or Pierpont primes of the second kind


 
import java.math.BigInteger;
import java.text.NumberFormat;
import java.util.ArrayList;
import java.util.List;
 
public class PierpontPrimes {
 
    public static void main(String[] args) {
        NumberFormat nf = NumberFormat.getNumberInstance();
        display("First 50 Pierpont primes of the first kind:", pierpontPrimes(50, true));
        display("First 50 Pierpont primes of the second kind:", pierpontPrimes(50, false));
        System.out.printf("250th Pierpont prime of the first kind:     %s%n%n", nf.format(pierpontPrimes(250, true).get(249)));
        System.out.printf("250th Pierpont prime of the second kind: %s%n%n", nf.format(pierpontPrimes(250, false).get(249)));
    }
 
    private static void display(String message, List<BigInteger> primes) {
        NumberFormat nf = NumberFormat.getNumberInstance();
        System.out.printf("%s%n", message);
        for ( int i = 1 ; i <= primes.size() ; i++ ) {
            System.out.printf("%10s  ", nf.format(primes.get(i-1)));
            if ( i % 10 == 0 ) {
                System.out.printf("%n");
            }
        }
        System.out.printf("%n");
    }
 
    public static List<BigInteger> pierpontPrimes(int n, boolean first) {
        List<BigInteger> primes = new ArrayList<BigInteger>();
        if ( first ) {
            primes.add(BigInteger.valueOf(2));
            n -= 1;
        }
 
        BigInteger two = BigInteger.valueOf(2);
        BigInteger twoTest = two;
        BigInteger three = BigInteger.valueOf(3);
        BigInteger threeTest = three;
        int twoIndex = 0, threeIndex = 0;
        List<BigInteger> twoSmooth = new ArrayList<BigInteger>();
 
        BigInteger one = BigInteger.ONE;
        BigInteger mOne = BigInteger.valueOf(-1);
        int count = 0;
        while ( count < n ) {
            BigInteger min = twoTest.min(threeTest);
            twoSmooth.add(min);
            if ( min.compareTo(twoTest) == 0 ) {
                twoTest = two.multiply(twoSmooth.get(twoIndex));
                twoIndex++;
            }
            if ( min.compareTo(threeTest) == 0 ) {
                threeTest = three.multiply(twoSmooth.get(threeIndex));
                threeIndex++;
            }
            BigInteger test = min.add(first ? one : mOne);
            if ( test.isProbablePrime(10) ) {
                primes.add(test);
                count++;
            }
        }
        return primes;
    }
 
}
 