Augusto Santi's user avatar
Augusto Santi's user avatar
Augusto Santi's user avatar
Augusto Santi
  • Member for 4 years, 2 months
  • Last seen more than a month ago
  • San Marino
13 votes
1 answer
1k views

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

10 votes
1 answer
465 views

Asymptotic behavior of a certain sum of ratios of consecutives primes

10 votes
0 answers
201 views

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

7 votes
1 answer
1k views

Some interesting experimental results about the distribution of primes

5 votes
1 answer
164 views

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

4 votes
0 answers
228 views

On the density of a particular subset of integers

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 $(3,24)$?

3 votes
1 answer
133 views

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

3 votes
1 answer
266 views

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

3 votes
1 answer
176 views

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

2 votes
2 answers
328 views

Arithmetic progressions of gaussian primes

2 votes
1 answer
289 views

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

2 votes
0 answers
156 views

Questions about a certain sequence of naturals generated by primorials

2 votes
0 answers
109 views

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

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?

2 votes
0 answers
154 views

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

1 vote
0 answers
175 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 $n\in\mathbb{N}$?

1 vote
1 answer
107 views

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

1 vote
0 answers
81 views

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

1 vote
0 answers
142 views

About the distribution of Fibonacci numbers that are primes

1 vote
0 answers
152 views

Euler product over subsets of primes

1 vote
0 answers
72 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

1 vote
1 answer
164 views

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

0 votes
0 answers
128 views

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

0 votes
0 answers
141 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 $\,g(2n)=n$

0 votes
1 answer
134 views

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

0 votes
0 answers
106 views

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

-1 votes
1 answer
281 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?

-1 votes
1 answer
304 views

About Landau's 4th problem

-3 votes
1 answer
178 views

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