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Proof of hypothesis of twin primes (important step: choosing a suitable interval)
Twin primes supremum infimum
2015/6/2
1. Distributive law of primes: (x/㏒x)㏒e＜π(x)≤(x/㏒x) ㏒11330／113, (11≤x＜∞); 2. Shortest suitable interval, [11, 19]; 3. Expression of twin odd numbers, ︱2x－11,…,…,…,4x－27︱ ︱2x－ 9,…,…,…,4x－25︱, Number of...
The proofs of twin prime conjecture and weaker Polignac's conjecture
prime distribution of primes twin primes Polignac's conjecture Goldbach-type problem
2011/9/18
This paper advanced a new method of appointedly covering prime circles with level colors of black degree, and showed twin prime conjecture and weaker Polignac's conjecture to be true with the proof by...
The Skewes number for twin primes: counting sign changes of $π_2(x)-C_2 \Li_2(x)$
Primes twins Skewes number Number Theory
2011/9/6
Abstract: The results of the computer investigation of the sign changes of the difference between the number of twin primes $\pi_2(x)$ and the Hardy--Littlewood conjecture $C_2\Li_2(x)$ are reported. ...
On twin and anti-twin words in the support of the free Lie algebra
On twin anti-twin words the free Lie algebra
2010/11/11
Let $L_{K}(A)$ be the free Lie algebra on a finite alphabet $A$ over a commutative ring $K$ with unity. For a word $u$ in the free monoid $A^{*}$ let $\tilde{u}$ denote its reversal. Two words in $A^...
Twin-vortex solitons in nonlocal nonlinear media
Twin-vortex solitons nonlocal nonlinear media
2010/4/1
We consider soliton formation in thermal nonlinear media bounded by rectangular cross-sections and uncover a new class of nonlinear stationary topological state. Specifically, we find that stationary ...