Newer Facets of Prime Number Theory

ISBN-13: 9783844306651 / Angielski / Miękka / 2011 / 120 str.

Opis

Since ancient times connoisseurs of number theory are fascinated by the prime-composite classification of natural numbers, but the law governing their distribution could not be discovered. This problem was also highlighted by CF Gauss by stating: the dignity of the science itself seems to require that every possible means be explored for the solution of the problem so elegant and so celebrated. This monograph provides the solution to this problem by studying primes via composite numbers and, interestingly, it is simple enough to be understood even by under-graduates. The formula so obtained has found several applications, while leaving further scope for the specialists. Thus, it meets the requirement of amateurs and specialists alike. APPLICATIONS : An effective algorithm for separating primes from composite numbers along with their prime factors developed; a new formula for number of primes up to any given integer sans approximation and hypothesis derived; Dirichlets prime number theorem modified; three prime conjectures proved; five new arithmetic functions introduced; some holistic probability-theoretic innovative ideas developed by going in to the genesis of the problems.

O autorze

Vishnu K Gurtu, PhD (1966, Allahabad Univ., India), Retd. Prof., LIT Nagpur Univ. (2000). Till 1988, worked in Astrophysics. Then switched over to Number Theory; solved many outstanding problems by going into their genesis. Presented proof of FLT consistent with its originator's thought-process and law for distribution of primes in ICMs, 2006, 2010