## Solving Polignac's and Twin Prime Conjectures Using Information-Complexity Conservation

**Authors:** John Yuk Ching Ting

Prime numbers and composite numbers are intimately related simply because the complementary set of composite numbers constitutes the set of natural numbers with the exact set of prime numbers excluded in its entirety. In this research paper, we use our 'Virtual container' (which predominantly incorporates the novel mathematical tool coined Information-Complexity conservation with its core foundation based on this [complete] prime-composite number relationship) to solve the intractable open problem of whether prime gaps are infinite (arbitrarily large) in magnitude with each individual prime gap generating prime numbers which are again infinite in magnitude. This equates to solving Polignac's conjecture which involves analysis of all possible prime gaps = 2, 4, 6,... and [the subset] Twin prime conjecture which involves analysis of prime gap = 2 (for twin primes). In conjunction with our cross-referenced 2017-dated research paper entitled "Solving Riemann Hypothesis Using Sigma-Power Laws" (http://viXra.org/abs/1703.0114), we advocate for our ambition that the Virtual container research method be considered a new method of mathematical proof especially for solving the 'Special-Class-of-Mathematical-Problems with Solitary-Proof-Solution'.

**Comments:** 21 Pages. This research paper outline the rigorous proofs for Polignac's and Twin prime conjectures. It is cross-related to Solving Riemann Hypothesis Using Sigma-Power Laws (http://viXra.org/abs/1703.0114).

**Download:** **PDF**

### Submission history

[v1] 2017-03-13 02:26:30

[v2] 2017-03-17 20:27:33

[v3] 2017-04-02 00:28:44

[v4] 2017-04-17 05:58:07

**Unique-IP document downloads:** 53 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*