Keywords:-

Keywords: Arithmetical progressions,block-wise distribution,prime, prime density, prime spacing.

Article Content:-

Abstract

Prime numbers exhibit many mysteries one of which is their distribution amongst the positive integers, for which yet there is no regular looking pattern recognized.
The simplest form being arithmetical progression, there have been consistent efforts to track their occurrences in these. As part of continued contribution to theseefforts, in this work prime numbers are analyzed with view of their distribution in the arithmetical progressions 6n + k.

References:-

References

Euclid (of Alexandria) (300 BC) , “Elements, Book IX”.

DirichletP. G. L. (1837), “Beweis des Satzes, dass jede unbegrenzte arithmetische

Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen

Factor sind, unendlich viele Primzahlen enthält”, Abhand. Ak. Wiss. Berlin.

Fine Benjamin, Rosenberger Gerhard (2007), “Number Theory: An Introduction via

the Distribution of Primes”, Birkhauser.

Granville Andrew, Martin Greg (2006), “Prime Number Races”, American

Mathematical Monthly 113 (1), pp. 1–33.

Pande Neeraj Anant (2015), “Improved Prime Generating Algorithms by Skipping

Composite Divisors and Even Numbers (Other Than 2)” Mathematics Section,

Journal of Science and Arts, Communicated. 6. Schildt Herbert (2006), “Java : The Complete Reference” 7th Edition, Tata McGraw –

Hill.

Downloads

Citation Tools

How to Cite
Pande, N. A. (2015). Analysis of Primes in Arithmetical Progressions 6n + K Up To A Trillion. International Journal Of Mathematics And Computer Research, 3(06), 1037-1053. Retrieved from https://ijmcr.in/index.php/ijmcr/article/view/119