To start let's use this trick to find a sequence of primes 11+13-7=17 This trick starts with prime 11 and the next in sequence 13. After you add them together to get 24 you subtract 7 which is the prime in sequence before 11, and you will get the answer 17. Now this will find every single prime imaginable but it also has a few holes. When you do this with 13+17-11=19 It still works well let's do it again 17+19-13=23 Again it works! One more time 19+23-17=25? What 25? That's not prime! But it is the factor of 5x5. Anyways lets get a little better idea 23+25-19=29 prime 25+29-23=31 prime 29+31-25=35 not prime but = to 7x5 The next holes are at: 7x7=49 5x11=55 5x13=65 7x11=77 5x17=85 The pattern to understand goes like this. I'll go to the first numbers under 100 Start at 1 add 4 1+4 (1 is not prime) 5+2 p 7+4 p 11+2 p 13+4 p 17+2 p 19+4 p 23+2 p 25+4 5x5 29+2 p 31+4 p 35+2 5x7 37+4 p 41+2 p 43+4 p 47+2 p 49+4 7x7 53+2 p 55+4 5x11 59+2 p 61+4 p 65+2 5x13 67+4 p 71+2 p 73+4 p 77+2 7x11 79+4 p 83+2 p 85+4 5x17 89+2 p 91+4 7x13 95+2 5x19 97+4 p When you do this you find every number that is prime and the smallest to largest factors of multiples of primes starting with 5x5. One thing to note is that the prime numbers "2 and 3" are not in the sequence, or at least apparent. Well that is if you don't know where to look. For every operation you have a +4 and a +2 4+2=6 6=2x3 Again two primes multiplied together. With all this information it is easy to develop a formula which will be (4x)+(2x)+1 (6x)+1 Plug whatever you want into this formula and you will find either a prime or a multiple of two primes. Now if you are a cryptographer and one of your friends has a password of two primes multiplied together just use this function and start with x=1000 and go find that password because you'll run across it soon enough. Like I said this will find you every prime you could ever want but knowing that it is a prime that you got for your answer instead of a composite number of two primes is a problem I can't even solve efficiently when it comes to truly large numbers. As you progress through you will find less and less primes because the combination of primes becomes larger and larger with every prime you find, but if you can figure it all out well I'm glad I helped, just let me know how you did it and we'll all be dandy.