The Human Genome Project which was almost mapped completely by 2003 provided basic understanding of human DNA and several non-humans DNA. It benefited the science of medicine for conquering diseases and genetic anomalies. On the other hand, the science of public key encryption and decryption of internet access still relies in some respect on the prime factorization of a large number. This large number is simply the product of two large semiprimes. The product as a key is found in the public domain while the secret keys are the prime factors which can remain almost intractable for the code breakers and can require years of computer calculations.
However, an unbreakable code would, still in some ways, necessarily uses prime numbers. But instead of multiplications of primes, it uses differences of primes. This can be done by combining Goldbach conjecture with Erdös conjecture, such that there are three prime numbers: a, b, and c where c > b and b > a. They are related by the simple formula such that: a = ˝(c-b). For example if a = 2, then there are infinite number of pairs of (b, c) as solutions to the formula: the first 5 are (3, 7), (13, 17), (37, 41), (43, 47), and (67, 71). If a = 3 then these become: (5, 11), (11, 17), (13, 19), (17, 23), and (23, 29). If a = 5 then these are: (3, 13), (7, 17), (13, 23), (19, 29), and (31, 41). If a = 7 then these are: (3, 17), (5, 19), (17, 31), (23, 37), and (29, 43). The prime number a can be the public key while b and c are the secret keys which wherever and whenever permutated and combined become truly unbreakable.


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