# Bounded gaps between primes

### Bounded gaps between primes

'Bounded gaps between primes':

"It is proved that

$$\lim inf_{n \to \infty}(p_{n+1 } - p_{n } ) < 7 * 10^{7}$$,

where $$p_{n}$$ is the n-th prime.

Our method is a refinement of the recent work of Goldston, Pintz and Yildirim on the small

gaps between consecutive primes. A major ingredient of the proof is a stronger version of the

Bombieri-Vinogradov theorem that is applicable when the moduli are free from large prime

divisors only (see Theorem 2 below), but it is adequate for our purpose..." -- Yitang Zhang,

Guest

### Re: Bounded gaps between primes

Guest wrote:'Bounded gaps between primes':

"It is proved that

$$\lim inf_{n \to \infty}(p_{n+1 } - p_{n } ) < 7 * 10^{7}$$,

where $$p_{n}$$ is the n-th prime.

Our method is a refinement of the recent work of Goldston, Pintz and Yildirim on the small

gaps between consecutive primes. A major ingredient of the proof is a stronger version of the

Bombieri-Vinogradov theorem that is applicable when the moduli are free from large prime

divisors only (see Theorem 2 below), but it is adequate for our purpose..." -- Yitang Zhang,

A Comment:

If true, that so-called celebrated result (bounded gaps between primes) of Yitang Zhang is a very weak result, and I am not impressed. And therefore, I never made the effort to review his long paper. And that Polymath project to improve on his result is also not impressive...

The twin prime conjecture and the Riemann Hypothesis give a big hint at the relevant truth.

And If one can prove the twin prime conjecture, the Riemann Hypothesis, or a weaker form of the Polignac conjecture, then that result will be a truly celebrated result.

My work on the Riemann Hypothesis and the Polignac conjecture has convinced me that they are true! And work is listed on this website too.

Dave.
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Guest

### Re: Bounded gaps between primes

Why would the twin prime conjecture or the more general Polignac conjecture be true?

Primes or prime divisors generate the all composite integers most efficiently in accordance with the Fundamental Theorem of Arithmetic and in accordance with the Prime Number Theorem.

Moreover, the repetition of gaps and the growth of gaps between consecutive primes or prime divisors are therefore essential for the efficient generation of all composites in accordance with the Fundamental Theorem of Arithmetic and in accordance with the Prime Number Theorem.

Hence, that is why I believe Yitang Zhang's result is very weak since there's no number bigger than infinity. A prime gap of $$10^{100000000000000000}$$ or much much much ... larger between consecutive primes is insignificant when compared with the infinity of the ordered primes along the natural number line.

Dave.
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Guest

### Re: Bounded gaps between primes

Hence, that is why I believe Yitang Zhang's result is very weak since there's no number bigger than infinity. A prime gap of $$10^{100000000000000000}$$
or much much much ... larger between consecutive primes is insignificant when compared with the infinity of the ordered primes along the natural number line and is also insignificant when compared with the gaps approaching infinity between some of those consecutive ordered primes too.
Guest

### Re: Bounded gaps between primes

"No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect, yet no other concept stands in greater need of clarification than that of the infinite." -- David Hilbert.

...Hence, that is why I believe Yitang Zhang's result is very weak since there's no number bigger than infinity. A prime gap of $$10^{100000000000000000}$$
or much much much ... larger between consecutive primes is insignificant when compared with the infinity of the ordered primes along the natural number line and is also insignificant when compared with the gaps approaching infinity between some of those consecutive ordered primes too.
.

Dave.
Guest

### Re: Bounded gaps between primes

Minor Update:

Guest wrote:Why would the twin prime conjecture or the more general Polignac conjecture be true?

Primes or prime divisors generate all composite integers or all composites most efficiently in accordance with the Fundamental Theorem of Arithmetic and in accordance with the Prime Number Theorem.

Moreover, the repetition of gaps and the growth of gaps between consecutive primes or prime divisors are therefore essential for the efficient generation of all composites in accordance with the Fundamental Theorem of Arithmetic and in accordance with the Prime Number Theorem.

Hence, that is why I believe Yitang Zhang's result is very weak since there's no number bigger than infinity. A prime gap of $$10^{100000000000000000}$$ or much much much ... larger between consecutive primes is insignificant when compared with the infinity of the ordered primes along the natural number line and is also insignificant when compared with the gaps approaching infinity between some of those consecutive ordered primes too...

Dave.
Guest