The difference of two prime consecutive prime numbers is the prime gap. $g_i := p_{i+1} - p_i$.
Questions tagged [prime-gaps]
407 questions
5
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1 answer
Why does the ninth successive difference of primes appear to have two distinct groups?
Was exploring successive differences of primes and noticed an interesting pattern of the histogram of counts for the sixth and ninth difference. The ninth is more pronounced, code and image below.
Mathematica code:
n = 5000000; (* First n primes…
sheppa28
- 929
3
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0 answers
When is the earliest large prime gap also the latest large prime gap?
Suppose one finds the earliest prime gap of at least a certain size $g$, so that $p_{n+1}-p_n=g$ and $n$ is the smallest index for which the gap is as big as $g$.
Now consider the relative size of the gap: $\dfrac{p_{n+1}-p_n}{p_n}$
When will $n$ be…
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a prime is a midpoint of two primes
Take three consecutive primes $p_1,p_2,p_3$:
What is the opinion on the question that
$p_3-p_2=p_2-p_1$ occurs endlessly and is harder to find as the primes increase?
Has anyone examined the frequency of these cases as the primes increase?
J. M. Bergot
- 912
1
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2 answers
Two kinds of prime gaps
$$1361 - 1327 = 34$$
Between these two prime numbers there are no others. No prime gaps this big come before this one; i.e. this one is "maximal".
The largest prime not exceeding the square roots of any of them is $31.$ All prime numbers not…
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1 answer
Can someone offer an overview of the idea of the proof of prime gaps bounds?
I saw on a YouTube video that Yitang Zhang's original proof was too sophisticated but a British mathematician called James Maynard, later proposed a more elementary proof that sharpened the upper bound to 600. The person said that Maynard's proof…
Saikat
- 2,461
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2 answers
Gaps between consecutive pairs of twin primes.
One can have a gap of $4$ between consecutive pairs of twin primes
as in $17-13=4$ for twins $(11,13)$ and $(17,19)$. There is also a gap of $10$ between $19$ and $29$ in twins $(17,19)$ and $(29,31)$ were it not for $23; 19$ and $29$ are not…
J. M. Bergot
- 912