4
votes
1answer
139 views

Relationship between Primes and Fibonacci Sequence

I recently stumbled across an unexpected relationship between the prime numbers and the Fibonacci sequence. We know a lot about Fibonacci numbers but relatively little about primes, so this connection ...
1
vote
2answers
89 views

How can I solve this problem without having to do it by hand?

I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement without forcing me to do it ...
0
votes
1answer
73 views

How can I solve this problem without doing it by hand? [duplicate]

I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement without forcing me to do it ...
1
vote
2answers
78 views

Is there any way to solve this problem without having to do it by hand? [duplicate]

I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement. Is there any way to group ...
5
votes
1answer
142 views

Zhang's theorem and Polignac's conjecture

Yitang Zhang made a groundbreaking discovery when he proved that there are infinitely many pairs of prime numbers which differ by less than $70,000,000$. Zhang's theorem has been significantly ...
2
votes
2answers
89 views

State of art of prime numbers distribution [closed]

I was reading some questions about prime numbers posted in latest days and a question came to my mind: What is the state of art of the research into prime numbers distribution? I read then ...
4
votes
1answer
202 views

Can the twin prime conjecture be solved in this way?

After some research, I have discovered that proving the statement; There exist an infinite number of positive integers K such that; $K \neq 6ab \pm a \pm b$ and $K \neq 6ab \mp a \pm b$ is ...
2
votes
0answers
92 views

When is a number like “ddd…ddd”+1 (where d is a digit) a perfect square or a prime?

Inspired by Is the number $333, 333, 333, 333, 333, 333, 333, 333, 334$ a perfect square?, I wonder when numbers like these are perfect squares. Certainly, all numbers of the form $000...0001$ are ...
2
votes
0answers
105 views

Are there infinitely many primes $p_k$ such that $(p_k-1)!+p_k$ is a also prime?

I am wondering whether there are infinitely many primes $p_k$ such that $(p_k-1)!+p_k$ is also prime. Given that $p_k \equiv 2 \pmod 3$. For a very large prime, I can assume Stirling's ...
18
votes
2answers
7k views

Has anyone found a “pattern” in prime numbers?

Yesterday I was having some fun trying to look for some patterns in primes; and I think I found something interesting (to me at least). I still have not found any lists of patterns already found, ...
3
votes
2answers
326 views

Are there infinitely many primes of the form $6^{2n}+1$ or only finitely many?

Does anyone know whether there are only finitely many of primes of the form $6^{2n}+1$, where $n$ zero or any natural number?
8
votes
0answers
204 views

Weak version of Fortune's conjecture

Let $p\#=2\cdot3\cdot5\cdots p$ denote the primorial and $N(x)$ the smallest prime greater than or equal to $x$. Then Fortune's conjecture is that $N(p\#+2)-p\#$ is prime for all $p$. (Heuristic: to ...
20
votes
4answers
3k views

Primes of the form $n^2+1$ - hard?

I met a student that is trying to prove for fun that there are infinitely many primes of the form $n^2+1$. I tried to tell him it's a hard problem, but I lack references. Is there a paper/book ...