User Augusto Santi

13 votes

1 answer

1k views

About the number of primes which are the sum of 3 consecutive primes (OEIS A034962)

asked Mar 3, 2020 at 18:39

10 votes

1 answer

469 views

Asymptotic behavior of a certain sum of ratios of consecutives primes

asked Feb 3, 2020 at 22:34

10 votes

0 answers

205 views

Does the diophantine equation $\,\prod_{k=1}^n(p_k^{x_k}-1)=y^2\,$ have always at least a solution for $\,n\gt2\,$?

asked Dec 26, 2020 at 20:39

7 votes

1 answer

1k views

Some interesting experimental results about the distribution of primes

asked Mar 31, 2020 at 23:10

5 votes

1 answer

167 views

Representation of primes of the form $4m+3$ with double radicals

asked Feb 5, 2020 at 20:32

4 votes

0 answers

232 views

On the density of a particular subset of integers

asked Feb 19, 2022 at 22:43

3 votes

1 answer

217 views

Does the equation in positive integers $(n,y)\,\prod_{k=1}^n(p_k^2-1)=y^2\,$ only have the solution $(3,24)$?

asked Dec 27, 2020 at 11:26

3 votes

1 answer

134 views

Is it possible to find an estimate of $\sum_{k=1}^n\frac1{\varphi(k\cdot p_k)}$?

asked May 26, 2021 at 20:02

3 votes

1 answer

277 views

Solutions in primes of the equation $\,3p^2+q^2=r^2+3$

asked Feb 23, 2020 at 15:44

3 votes

1 answer

188 views

About the sum $S(p_n)=\sum_{1\le k\lt n}\,p_n\mod\;p_k$

asked Mar 21, 2020 at 22:43

3 votes

2 answers

361 views

Arithmetic progressions of gaussian primes

asked Aug 20, 2020 at 19:06

2 votes

1 answer

384 views

Convergence of series $\sum_{k=1}^{\infty}\frac{p_{k+1}-p_k}{(p_{k+1}+p_k)^\alpha}$

asked Feb 4, 2020 at 22:15

2 votes

0 answers

156 views

Questions about a certain sequence of naturals generated by primorials

asked Feb 8, 2020 at 22:21

2 votes

0 answers

114 views

A conjectured upper bound for the mean value of prime divisors inside prime gaps

asked Nov 11, 2020 at 19:18

2 votes

0 answers

94 views

How far ahead do we have to look after $p_n$ to be sure we find another prime $q$ such that $(p_n+q)/2$ is also prime?

asked Dec 6, 2020 at 21:04

2 votes

0 answers

156 views

The recurrence relation $x_{n+1}=x_{n}+x_{n-1}+c\,(x_{n},\,x_{n-1})$

asked Dec 30, 2021 at 10:39

1 vote

0 answers

178 views

Given a prime $\,p\ne3$, is it always possible to find another prime q such that $\,\phi(q)=\phi(p\cdot2^{2n+1})\,$ for some $n\in\mathbb{N}$?

asked Mar 18, 2020 at 4:36

1 vote

1 answer

123 views

Periodic sequences of integers generated by $a_{n+1}=\frac{\operatorname{rad}(pa_{n})}{p}+\frac{\operatorname{rad}(qa_{n-1})}{q}$

asked May 20, 2022 at 21:11

1 vote

0 answers

81 views

An upper bound for $\,m_k=\min\,\{m\in N:\,mp_k+1\;\;is\;prime\}$

asked Dec 27, 2020 at 17:22

1 vote

0 answers

148 views

About the distribution of Fibonacci numbers that are primes

asked Mar 23, 2020 at 22:27

1 vote

0 answers

166 views

Euler product over subsets of primes

asked May 17, 2020 at 21:05

1 vote

0 answers

73 views

How we can characterize all positive integers, multiples of 4, that cannot be expressed as $(p_1-1)(p_2-1),\;\;p_1,\,p_2$ distinct primes

asked May 21, 2020 at 21:10

1 vote

1 answer

181 views

Density of gaussian primes inside consecutive disks centered along the real axis of complex plane

asked Aug 20, 2020 at 13:59

0 votes

0 answers

133 views

A quadratic trinomial that generates only prime numbers of the form $4m+1$

asked Mar 28, 2020 at 22:29

0 votes

0 answers

143 views

Given $\,m=\prod_k {p_k}^{\alpha_k}\,$ and the function $\,g(m)=\sum_k \alpha_k(p_k-1)^2$, find all solutions of the equation $\,g(2n)=n$

asked Mar 5, 2020 at 22:38

0 votes

1 answer

137 views

Search for gaps between primes where each composite is divisible by increasing integers (2, 3, 4, ...)

asked Dec 28, 2020 at 21:52

0 votes

0 answers

112 views

The number of solutions of $2^xpx+k=y^2$

asked Jun 4, 2021 at 17:36

-1 votes

1 answer

283 views

Is it possible to determine whether the sequence $\,a_0=p,\;a_{n+1}=(a_n-2)\cdot a_n+2\,$ will reach another prime number?

asked Mar 12, 2020 at 23:30

-2 votes

1 answer

355 views

About Landau's 4th problem

asked Nov 8, 2020 at 22:26

-3 votes

1 answer

178 views

Asymptotic behavior of $\sum_{k=1}^{n}\frac{p_{k+1}}{p_{k+1}-p_k}$

asked Feb 4, 2020 at 7:15

Stack Exchange Network

30 Questions

About the number of primes which are the sum of 3 consecutive primes (OEIS A034962)

Asymptotic behavior of a certain sum of ratios of consecutives primes

Does the diophantine equation $\,\prod_{k=1}^n(p_k^{x_k}-1)=y^2\,$ have always at least a solution for $\,n\gt2\,$?

Some interesting experimental results about the distribution of primes

Representation of primes of the form $4m+3$ with double radicals

On the density of a particular subset of integers

Does the equation in positive integers $(n,y)\,\prod_{k=1}^n(p_k^2-1)=y^2\,$ only have the solution $(3,24)$?

Is it possible to find an estimate of $\sum_{k=1}^n\frac1{\varphi(k\cdot p_k)}$?

Solutions in primes of the equation $\,3p^2+q^2=r^2+3$

About the sum $S(p_n)=\sum_{1\le k\lt n}\,p_n\mod\;p_k$

Arithmetic progressions of gaussian primes

Convergence of series $\sum_{k=1}^{\infty}\frac{p_{k+1}-p_k}{(p_{k+1}+p_k)^\alpha}$

Questions about a certain sequence of naturals generated by primorials

A conjectured upper bound for the mean value of prime divisors inside prime gaps

How far ahead do we have to look after $p_n$ to be sure we find another prime $q$ such that $(p_n+q)/2$ is also prime?

The recurrence relation $x_{n+1}=x_{n}+x_{n-1}+c\,(x_{n},\,x_{n-1})$

Given a prime $\,p\ne3$, is it always possible to find another prime q such that $\,\phi(q)=\phi(p\cdot2^{2n+1})\,$ for some $n\in\mathbb{N}$?

Periodic sequences of integers generated by $a_{n+1}=\frac{\operatorname{rad}(pa_{n})}{p}+\frac{\operatorname{rad}(qa_{n-1})}{q}$

An upper bound for $\,m_k=\min\,\{m\in N:\,mp_k+1\;\;is\;prime\}$

About the distribution of Fibonacci numbers that are primes

Euler product over subsets of primes

How we can characterize all positive integers, multiples of 4, that cannot be expressed as $(p_1-1)(p_2-1),\;\;p_1,\,p_2$ distinct primes

Density of gaussian primes inside consecutive disks centered along the real axis of complex plane

A quadratic trinomial that generates only prime numbers of the form $4m+1$

Given $\,m=\prod_k {p_k}^{\alpha_k}\,$ and the function $\,g(m)=\sum_k \alpha_k(p_k-1)^2$, find all solutions of the equation $\,g(2n)=n$

Search for gaps between primes where each composite is divisible by increasing integers (2, 3, 4, ...)

The number of solutions of $2^xpx+k=y^2$

Is it possible to determine whether the sequence $\,a_0=p,\;a_{n+1}=(a_n-2)\cdot a_n+2\,$ will reach another prime number?

About Landau's 4th problem

Asymptotic behavior of $\sum_{k=1}^{n}\frac{p_{k+1}}{p_{k+1}-p_k}$