Primed for perfection

By: Josh Leach


     What is so special about prime numbers?  Why have so many mathematicians sought to find a pattern in prime numbers?  Well, primes have some applications in upper mathematics, but their use in programming and cryptography has made them extremely important.
     One way people protect the security of personal or secret information is by encrypting it.  Programmers often use prime numbers in the encrypting process.  The unique way they convert data into primes is called a key.  When the data is transferred across the internet, only someone with the same key can reverse the encryption.  However, if someone cracked the prime number pattern, these security measures would be rendered void.  Any data encrypted with prime numbers would be left completely unprotected.  Abby Aldridge, a senior at Seckman High School, said, “I’m surprised that our entire digital world could come crashing down by some clever mathematician. ”Prime numbers have a variety of other applications involving programming.  For example, primes can be used for pseudo random generators.  According to MathOverflow.com, primes can also be used for “hard disks interleaving, error correction codes, and the lengths of hash functions.”
     A complete prime number pattern has not been found, but some minor patterns have been observed.  Euclid, a famous mathematician, did a lot of work with primes and was the first to prove that an infinite number of primes exist.  Later, prime number spirals were discovered.  They found that primes tend to be solutions to certain quadratic equations, such as x2 + x + 17 and 4x2 + 2x + 17.  Quite recently, according to Lisa Zyga from Phys.org, “They found that the distribution of the leading digit in the prime number sequence can be described by a generalization of Benford’s law.”  However, Logan Smith, a senior, said, “Mathematicians have devoted a lot of effort to figuring out primes.  If they have done so by now, they probably never will.”
     Prime numbers have always fascinated curious mathematicians.  People even found many applications for prime numbers in programming and upper math.  However, a complete pattern for primes continues to elude mathematicians.  Perhaps primes are fundamental random.  Many people hope this is true, because otherwise a dramatic change in cryptographic techniques may be necessary.