Are There Infinitely Many Twin Primes ?
نویسنده
چکیده
Is this observation a true fact? Certainly it is easy to verify that no matter where you look among the numbers you find plenty of primes. From a scientific point of view you can do billions of experiments with your mathematical package and always find primes. It can be tested more often and more precisely than any law of physics. You can safely bet the family farm on this and still sleep soundly at night. And yet, I think many of you will agree with me that in this case scientific observation and experimental evidence is a sorry excuse for real knowledge. It may be acceptable for a court of law or everyday life, but it is totally unacceptable given that you can use pure logical reasoning and a few basic axioms for numbers to conclude that this is not just an empirical observation, but a fact built into the structure of whole numbers themselves. It was the genius of the ancient Greeks to develop mathematics not just as an empirical science, but as an axiomatic system for logical deductions. In Euclid we find in place of the above scientific observation the following deduction.
منابع مشابه
Research Statement Dominic Klyve
My research concerns explicit inequalities in elementary number theory. Specifically, I am interested in the distribution of twin primes, along with theoretical and computational techniques for putting explicit bounds on classes numbers such as twin primes. One important method I use to examine the density of twins is to look for bounds on Brun’s Constant. 1. Motivation and Background Twin prim...
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