Tip of the Iceberg :: SnTT: Mersenne Primes

Category show-n-tell thursday
Roughly 9 years ago, a contractor (who I never met) at the company where I worked at the time was fired for installing a grid program on a bunch of company computers in the hopes of discovering a new prime number. It brought the network to its knees. I don't know what reminded me of that, but I started thinking about how one would go about testing a number's primality in LotusScript. For low numbers, it's quite easy:

Let PotentialPrime = (2 ^ Exponent) - 1
Let IsPrime = True 'Assume prime until proven otherwise
For Divisor = 2 To Fix(dblIsPrime / 2)
    If (PotentialPrime Mod Divisor = 0) Then
        Let IsPrime = False
        Exit For
    End If
Next

Of course, LotusScript has pretty low limits to number storage... even when using Doubles, you get an Overflow pretty rapidly. Just for fun, I did a little reading and stumbled upon the concept of Mersenne Primes: basically, since all prime numbers higher than 2 are odd, 2ⁿ - 1 tends to be prime if n is also prime. But not always... so the "Lucas-Lehmer test" is a formula for determining whether or not a number conforming to this pattern is in fact prime. I found a Java implementation of that formula, pulled it into a script library in a Notes database, modified the main function to make it a static boolean instead of running as a command line program, then wrote a background thread agent to test exponents and create a document for any that produce a valid Mersenne:

import lotus.domino.*;
import java.math.BigInteger; // for determining probable primality of exponents

public class JavaAgent extends AgentBase {
    public void NotesMain() {
        try {
            Session session = getSession();
            AgentContext agentContext = session.getAgentContext();
            Database dbCurrent = agentContext.getCurrentDatabase();
            View vwPrimes = dbCurrent.getView("Primes");
            Document docLastFound = vwPrimes.getFirstDocument(); // pick up where we left off last time
            int intExponent = docLastFound.getItemValueInteger("Exponent") + 2; // only works for odd exponents
            int intPrimesFound = 0;
            while (intPrimesFound < 128) { // only 44 have been found so far, so this could take a while
                BigInteger possiblePrime = new BigInteger(new Integer(intExponent).toString());
                if (possiblePrime.isProbablePrime(1)) { // don't bother checking an exponent if it isn't prime to begin with
                    if (LucasLehmer.isPrime(intExponent)) {
                        docLastFound = dbCurrent.createDocument();
                        docLastFound.replaceItemValue("Form","Prime");
                        docLastFound.replaceItemValue("Exponent",new Integer(intExponent)); // Notes won't store an int
                        docLastFound.save(true,true,true);
                        intPrimesFound++;
                        System.out.println("Lucas approves of exponent " + intExponent);
                    }
                }
                intExponent += 2; // grab the next odd exponent
            }
        } catch(Exception e) {
            e.printStackTrace();
        }
    }
}