Questions tagged [prime-constellations]
On certain subsets of prime numbers which are consecutive and close. Prime twins $p$ and $p+2$, as well as $p-2, p, p+4$, are constellations. Also related are admissible sets in number theory, which are sets $A$ of integers $a_i$ such that there may be an integer $t$ with many or all of $t+a_i$ being prime. This has ties to prime gaps and additive number theory
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Symmetry in Hardy-Littlewood k-tuple conjecture
Assuming Hardy-Littlewood $k$-tuple conjecture, do the "dual" prime constellations $(0,h_1, h_2,\cdots, h_i,\cdots, h_{k-1}=d)$ and $(0, h_{k-1}-h_{k-2}, h_{k-1}-h_{k-3},\cdots,h'_i=h_{k-1}-...
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Do prime gaps that are a power of "h" have the same density?
Send me back to Mathematics Stack Exchange if this question is not research level.
At Terence Tao's blog post there is the expression:
$$\sum\limits_{n \leq X} \Lambda(n)\Lambda(n+h) \ \ \ \ \ \ \ \ \ ...
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On $\sum_{\substack{p\leq x\\p,p+2\text{ twin primes}}}\frac{(\log p)^m}{p}$, on assumption of the first Hardy–Littlewood conjecture
I wondered, inspired in a result from [1] (Proposition 17) what should be the asymptotic behaviour of the sequence, on assumption of the First Hardy–Littlewood conjecture,
$$\sum_{\substack{\text{...
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Do $k$ specific prime factors uniquely determine the continuous composite sequence of length $k$?
猜想:不存在两个长度为k且一共含有k个不同素因子的连续合数序列的素因子集合相等。例如
24 25 26 27 (2 3 5 13)
其余长度为4的连续合数序列要么素因子个数大于4 要么素因子集合不等于{2 3 5 13} 这个连续合数猜想的重大特定情况下的猜想。难度可与哥德巴赫猜想匹敌，非天才误入。再比如2 3 5 唯一决定了8 9 10 除此之外再无其他。总之经过计算机验证没有找到反例。
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