Clarkson University Honors Program Thesis Proposal
Methods for Predicting Prime Numbers
Matthew McClure
Christino Tamon, Advisor
March 8, 2000
A prime number is an integer that is divisible only by one and itself. Despite this simple
definition, there is no formula to predict where prime numbers will occur. Many different methods have
been developed to predict primes, each with different strengths and limitations. One common trait of
these methods is that none of them are very elegant in a purely mathematical sense. All of them require
computers to perform millions of repetitive calculations, or "brute force" calculations. Improving the
efficiency of current methods would be of great importance to the mathematical community.
The occurrence of prime numbers is much more than a purely intellectual pursuit. Cryptography
is one of the more practical applications of prime numbers. Cryptography is dependant upon processes
which are easily computed, but the reverse of which is very difficult to compute. Multiplying two primes
together is a simple computation, but finding the factors of that composite number requires brute force
computations.
My goals for this thesis are very humble. Realizing that prime number theory has been beaten to
death by several of the greatest minds in mathematics, I do not intend to "crack the secret of prime
numbers." My research will be divided into two parts that will overlap heavily. They are described
below:
Goals and Methods:
Research/Learning New Skills:
1) Research current methods for predicting primes. Understand why they work and their relative strengths
and weaknesses.
2) Learn necessary computer software and programming languages (C++) to test methods for predicting
primes.
Analysis/Generation of New Methods:
1) Create composite methods from existing ones, drawing upon specific strengths of each method.
2) Attempt to generate new methods for predicting primes.
3) Test any new methods created and rate it's efficiency relative to current methods.