Fixed-Memory Prime Number Generator

A small utility that can generate prime numbers starting from “2” till infinity (if left running forever) WITHOUT using system processor or RAM for mathematical divisions involved. Moreover, it must be capable of handling a number which can be millions of digits in length, perform prime number checks over them and finally store them in a database for later research use. The code must be small enough to fit inside a microprocessor such as PIC18F452. Based upon Sieve of Eratosthenes, though, I did not know about sieve theory while developing this.