A new methodology for exploring the natural number system. Proof of Adrien Legendre's conjecture of primes between the square of two consecutive numbers. Proof of the twin prime conjecture, in the affirmative. More
A book or discourse, a long time in the making, focused on the singular question: do twin primes exist at infinity? A proof in the affirmative to this question is presented along with a one-page proof of Adrien Legendre's conjecture that there exist a prime between the square of a number and squared number that follows.
An introduction of terminology in the study of number theory; in particular, the study of the natural number system. Terms include: footprint, half footprint, footprint table, half of the half footprint, registered primes, leading primes, builder primes, and other terms specific to the methodology. Careful consideration has been given to the terminology so the student does not confuse this "problem specific" terminology with long established definitions for concepts such as neighborhoods, cardinality and compactness.
*All terms have precise definitions and examples are given for each.
Suggestions for further study are made. More results in number theory, that follow vacuously, are left to the reader or those that have long investigated them.
A light read for mathematicians, physicists, engineers, scientists and anyone with a love for number theoretic puzzles.
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