All Questions
Tagged with prime-number-theorem prime-gaps
7 questions
-3
votes
1
answer
201
views
Formula for gaps between primes [closed]
The twin prime conjecture refers to:
$$
\liminf_{n\to \infty}\; p_{n+1} - p_{n} = 2.
$$
By reasoning I arrive at the following simple formula for gaps between primes:
\begin{align}
p_{...
- 13
1
vote
0
answers
156
views
Nontrivial nonrandom properties of prime numbers
What are some nontrivial nonrandom properties of prime numbers. Consider the simple model where each number is prime with probability 1/log(n) by Montgomery and extensions of it. Once you add some ...
- 680
0
votes
2
answers
302
views
How can I convert Meissel's/Lehmer's formula for prime counting to get sum of primes
Legendre's formula can be very easily be generalised as mentioned here (visible after login) which is like this
${\pi}(v,p)={\pi}(v,p-1)-1.[{\pi}(v/p,p-1)-{\pi}(p-1,p-1)]$
${ \big\downarrow}$
$S(v,p)=...
- 103
1
vote
0
answers
186
views
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。
...
- 29
1
vote
1
answer
186
views
Comparing densities of different gapped primes (twin, cousin, sexy...) [closed]
In this experiment, I have checked how many times different gapped primes occur out of the first 10000, 100000, 1000000 first primes.
Please view the following as ($X$:$Y$) where $X$ represents the ...
- 123
-3
votes
1
answer
237
views
L. Gegenbauer's proof of Infinitude of Primes [closed]
I was going through the paper 'Euclid’S theorem on the infinitude of primes: A historical survey of its proofs' by Romeo Mestrovic where he mentioned that
L. Gegenbauer proved Infinitude of Primes by ...
- 233
0
votes
1
answer
228
views
Is this theorem on the abundance of prime patterns/k-tuples known?
I am looking for references regarding the following statement.
For any two natural numbers x and y there must be a prime k-tuple (a, b, ...) corresponding to x consecutive primes (n+a, n+b, ...) for ...