The technical paper containing *Prime Number Distribution Series (PNDS)* is now published^{1}.

Download Material:

*PNDS* – Mathematical Formula for Finding Prime Numbers, by Yoldas Askan^{2}.

*PNDS* – Sieve Verification C++ Open Source Code^{1}.

*PNDS* Non-sieving Executable^{3}.

*Prime Number Distribution Series (PNDS)*, developed by the *NSI* team of mathematicians^{2}, computes the **exact** count of primes below integer *N (N → ∞) (π (N))*. Aside from divide and count test and various sieving methods, it is believed that *PNDS* is the first and only exact mathematical formula for finding prime numbers.

*PNDS* demonstrates that a pattern of prime numbers exists; making fast evaluation of π (N) for large N at record speeds possible^{2}.

**Riemann Hypothesis**

As shown in the technical paper, neither *PNDS* nor its inverse is a complex variable function, and that *PNDS* uniquely produces exact count of prime numbers for a given integer *P*, where *2 < P < ∞*, it may be concluded that the distribution of prime numbers is not a complex variable problem and Riemann Zeta Function may not be pertinent to the subject matter.

**History**

Little or not at all considered fact is that the distribution of prime numbers can be regarded as *piecewise orderly*. For example, consider Euler prime formula, *P(n) = n2 − n + 41*. It is easy to show this function is asymptotic and strictly speaking only holds for *0 < n < 5*. Like Euler prime formula, infinitely many series can be formulated each representing prime number distribution at the boundary limits. We therefore conclude that no single series, of any order; equation or a function will ever yield prime numbers for all *n = 1* to *∞* exclusively.

Henceforward, Riemann conjecture that the *nontrivial zeros of the Riemann zeta function all have real part ½* is an irrelevant submission to the problem.

However, a series can be formulated that will produce the boundary values of the *piecewise orderly* regions for *N → ∞*; as given by the *PNDS* mathematical formula

**RSA Numbers, Public-key Cryptography and Online and Electronic Communication Security**

*PNDS* series, together with other numerical algorithms, may allow factorization of large bit *RSA* numbers with expected computing times of the order of few minutes on a single processor.

**Distribution List**

Mathematical contents of the work have been disclosed to the following:

NSI Patent Attorney, Oct 2013

The Open University, May 2014

Published, August 2014

CodeProject, Sept 2014

1. Copyright © 2014 Nuclear Strategy, Inc. All rights reserved. Use of contents is restricted for educational and research purposes only. Do not reproduce, redistribute or reference without the prior written permission of the publisher.

2. Prime Number Distribution Series (PNDS) is discovered by Yoldas Askan

2. Current version of the PNDS exe computes π (1e12) in less than 10 seconds using a 2.49GHz Processor i5 Windows 8 workstation. However, PNDS is temporarily limited to N = 1e8 (evaluated in 3 seconds) pending high *precision arithmetic library* implementation on Windows (such as GNU GMP). PNDS will subsequently be unrestricted for any N → ∞. Please note that PNDS exe can potentially compute π (1e25) in less than 1 minute with similar specification Windows machines. Minimum requirements for running PNDS exe are Windows 7 or Windows 8 i5 machines.