Algorithm writing tips?

Code:

private static ArrayLists primeList (single numbers only), other lists of sets of primes.

public static void main(String[] args){
    --Initialize the long nextPrime, to keep track of the new prime being checked every pass of the while(true) loop.
    --Initialize any other stuff as necessary.

    while(true){
        --Find the next prime number in the sequence primeList.  This is the new value of nextPrime.

        --Use nextPrime and concatenate with existing sets of primes (sets of four primes, three, then two) to see if they make larger sets of primes.
        --If a set of five primes is found, print out the results and return;
        --If ANY of the primes fail to concatenate with nextPrime to make a new prime number, the test fails, and the computer moves to the next set of primes.
        --If the set of primes passes the test, a new array for the larger set of primes is added to the corresponding ArrayList.  The old set of primes stays put.

        --Compare existing known primes with nextPrime to see if they make sets of two primes.  This is pretty much the only reason why primeList exists.
    }//end while(true) loop
}

Stereo, why would you set numbers concatenated with themselves as true? They aren't primes for the very obvious reason that they have a factor that is the parent prime. Other than that, I might take a look into your idea.

Oh yeah, you might have noticed a time variable. On the output, it said "Time: 134.60858333333334 minutes."