OK, I am new to this, but is there a simple test for a number being prime? The number obviously cannot end in an even number or with a five or a zero. So we eliminate testing division by 2, 4, 5, 6, 8, and 10 immediately. Any number divisible by 9 is also divisible by 3, so it seems the first tests are to find if the next number is divisible by 3, 7, 11, 13, 17, etc., to include other prime numbers as we progress. Does this make sense?
It seems that 1667 is the next number that passes these tests.