## Rigorous Proofs for 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' method, 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 "Rigorous proof for Riemann hypothesis using Sigma-Power Laws" http://viXra.org/abs/1703.0114, we advocate for our ambition that the Virtual container method be considered as a new method of mathematical proof especially for ’Special-Class-of-Mathematical-Problems with Solitary-Proof-Solution’.

**Comments:** 18 Pages. This research paper contains the rigorous proofs for Polignac's and Twin prime conjectures.

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### Submission history

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

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

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