Searching for Prime

Classical primality testing of large numbers requires a number to be rigorously divided by all prime numbers, up to the square root of the number to be tested. This method is time- and resource- consuming for large numbers. Some time is gained by only dividing by prime numbers to determine the factors, but this too falls short where large numbers are tested for which not all the required lower primes are known. The problem becomes no easier when the very next higher prime number is sought, because the entire rigorous process has to be repeated for every number, and the number of calculations increase as the numbers get bigger. A prime number is a positive integer that can only be fully divided by 1 and itself. Regarding primality, a positive integer can only have 2 states: prime or non-prime. It is one or the other, no inbetweens. If it can be proven that a number is not non-prime, it is inherently proven that it is prime. This is also the basis upon which the Sieve of Eratosthenes works [1]. A method is presented for finding prime numbers, “from the bottom up” thereby allowing the sieve to be expanded as new prime numbers are discovered. The number of calculations required is greatly reduced by using a quadratic relationship.