User so-called friend Don

41 votes

Computing $\prod_p(\frac{p^2-1}{p^2+1})$ without the zeta function?

answered Apr 23, 2014 at 15:08

23 votes

Accepted

Does the sum $\sum_{n=1}^{\infty}\frac{1}{p_n(p_{n+1}-p_n)}$ converge?

answered Feb 4, 2016 at 17:13

21 votes

Accepted

Does the least prime factor have a mean of some sort?

answered Sep 12, 2016 at 12:44

16 votes

Accepted

Roots of unity near 1 in Z / p Z

answered Apr 11, 2014 at 16:19

16 votes

Hecke equidistribution

answered Jun 12, 2013 at 1:20

15 votes

Accepted

A naive question about the prime number theorem

answered Apr 26, 2020 at 18:54

13 votes

Accepted

Are primes of density 0 in $a\cdot b^n+c$?

answered Jan 8, 2014 at 22:19

13 votes

Accepted

How frequently is 3 a cubic residue mod primes in an arithmetic progression?

answered Jul 17, 2014 at 5:29

11 votes

Is every number the sum of two cubes modulo p where p is a prime not equal to 7?

answered Oct 24, 2014 at 17:06

11 votes

Numbers $n$ such that the sum of the divisors of $n$ is a nontrivial power

answered Mar 24, 2015 at 14:26

11 votes

Accepted

Existence of relative Dirichlet density of primes starting with 1

answered Aug 7, 2017 at 22:41

11 votes

Sum of the reciprocals of radicals

answered Nov 16, 2018 at 3:22

10 votes

Accepted

Are there other integer solutions to the equation $9x^3 -1 = y^3$ besides $(x,y) =(1,2)$ and $(0, -1)$?

answered Dec 1, 2015 at 1:17

10 votes

Accepted

Does there exist an integer that is both solitary and almost perfect?

answered Mar 25, 2015 at 16:33

10 votes

Accepted

Asymptotics and error terms for an arithmetic function built upon $\omega$ and $\Omega$ functions

answered Jul 21, 2014 at 23:08

10 votes

Accepted

Proportion of square-free integers $n$ with $\gcd(n,\varphi(n))$ a prime

answered Jan 8, 2014 at 16:29

10 votes

Accepted

explicit lower bounds on $|L(1,\chi)|$

answered Nov 30, 2011 at 18:32

9 votes

About integer polynomials which are sums of squares of rational polynomials...

answered Nov 30, 2011 at 17:47

9 votes

Accepted

The density of numbers of the form $p + 2^k$

answered Nov 4, 2013 at 20:12

9 votes

Accepted

Squarefree parts of Mersenne numbers

answered Nov 29, 2013 at 17:12

9 votes

Accepted

How often is $2^n-1$ a number with few divisors?

answered Oct 19, 2015 at 4:09

9 votes

Accepted

Factorizations of cyclotomic polynomials valuated at primes

answered Sep 23, 2023 at 19:13

8 votes

Accepted

1/2 Wilson's theorem

answered Mar 30, 2019 at 1:32

8 votes

Is it possible to show that :for $n \geq 1:\sigma(n!-1) $ never be prime and why $\sigma(n!-1)\bmod 10 $ at most is $0$?

answered Nov 27, 2016 at 2:38

8 votes

Accepted

What is known about the largest prime divisor of the product of $k$ consecutive integers?

answered Oct 31, 2015 at 15:30

8 votes

Perfect powers in the solutions of a certain Pell equation

answered Nov 30, 2016 at 3:05

8 votes

Asymptotics of product of Euler's totient function (A001088)?

answered Feb 5, 2016 at 18:04

8 votes

Accepted

If the natural density (relative to the primes) exists, then the Dirichlet density also exists, and the two are equal

answered Feb 7, 2016 at 20:18

8 votes

Results on the largest prime factor of $2^n+1$

answered Aug 14, 2016 at 23:04

8 votes

Irreducible polynomials with a root modulo almost all primes

answered Dec 4, 2013 at 18:12

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66 Answers

Computing $\prod_p(\frac{p^2-1}{p^2+1})$ without the zeta function?

Does the sum $\sum_{n=1}^{\infty}\frac{1}{p_n(p_{n+1}-p_n)}$ converge?

Does the least prime factor have a mean of some sort?

Roots of unity near 1 in Z / p Z

Hecke equidistribution

A naive question about the prime number theorem

Are primes of density 0 in $a\cdot b^n+c$?

How frequently is 3 a cubic residue mod primes in an arithmetic progression?

Is every number the sum of two cubes modulo p where p is a prime not equal to 7?

Numbers $n$ such that the sum of the divisors of $n$ is a nontrivial power

Existence of relative Dirichlet density of primes starting with 1

Sum of the reciprocals of radicals

Are there other integer solutions to the equation $9x^3 -1 = y^3$ besides $(x,y) =(1,2)$ and $(0, -1)$?

Does there exist an integer that is both solitary and almost perfect?

Asymptotics and error terms for an arithmetic function built upon $\omega$ and $\Omega$ functions

Proportion of square-free integers $n$ with $\gcd(n,\varphi(n))$ a prime

explicit lower bounds on $|L(1,\chi)|$

About integer polynomials which are sums of squares of rational polynomials...

The density of numbers of the form $p + 2^k$

Squarefree parts of Mersenne numbers

How often is $2^n-1$ a number with few divisors?

Factorizations of cyclotomic polynomials valuated at primes

1/2 Wilson's theorem

Is it possible to show that :for $n \geq 1:\sigma(n!-1) $ never be prime and why $\sigma(n!-1)\bmod 10 $ at most is $0$?

What is known about the largest prime divisor of the product of $k$ consecutive integers?

Perfect powers in the solutions of a certain Pell equation

Asymptotics of product of Euler's totient function (A001088)?

If the natural density (relative to the primes) exists, then the Dirichlet density also exists, and the two are equal

Results on the largest prime factor of $2^n+1$

Irreducible polynomials with a root modulo almost all primes