Question

Find the upper bound and lower bound of the number of prime numbers less than x

score 183 · Answer 1 · 2018-02-27 14:13:52

183

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Find the upper bound and lower bound of the number of prime numbers less than x

Published on 27 Feb 2018 - 14:13

score 1.3k · Answer 2 · 2026-03-25 05:00:03

1.3k

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A solution using 'Lifting the exponent' lemma to IMO 1990 P3

Published on 25 Mar 2026 - 5:00

score 132 · Answer 3 · 2026-03-25 12:15:15

132

Views

Number Theoretic Estimate $\sum_{p\leq y}\frac{\log p}{p}h(pt)=\int_{t}^{yt}\frac{h(v)}{v}\ dv+O\big(h(y)\big)$

Published on 25 Mar 2026 - 12:15

score 881 · Answer 4 · 2026-03-25 06:19:51

881

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Let $\phi$ be Euler's totient function, find all $n$ such that $\phi(n) = \frac{1}{3} n$.

Published on 25 Mar 2026 - 6:19

score 905 · Answer 5 · 2026-03-25 05:02:12

905

Views

If $p$ is prime, with $p> 3$, then $p^{2} \equiv1\pmod{24}$

Published on 25 Mar 2026 - 5:02

score 320 · Answer 6 · 2026-03-23 09:01:21

320

Views

Bounding Maximal gaps with Ramanujan primes

Published on 23 Mar 2026 - 9:01

score 180 · Answer 7 · 2026-03-24 00:13:26

180

Views

Given a sufficiently large integer $N$, is it true that there are more primes than perfect squares in $[1,N]$?

Published on 24 Mar 2026 - 0:13

score 4.1k · Answer 8 · 2018-03-01 22:01:06

4.1k

Views

Prove that there are infinitely many primes of the form $6n + 5$

Published on 01 Mar 2018 - 22:01

score 274 · Answer 9 · 2026-03-25 06:29:19

274

Views

Prove that if $p$ is a prime number, then $p|n^p-n$

Published on 25 Mar 2026 - 6:29

score 51 · Answer 10 · 2018-03-02 10:12:15

51

Views

$n=2^k-1$ iff ${n \choose 1}, {n \choose 2}, ..., {n \choose n-1}$ are odd

Published on 02 Mar 2018 - 10:12

score 48 · Answer 11 · 2018-03-02 15:18:32

48

Views

NT Divisibility with Primes

Published on 02 Mar 2018 - 15:18

score 70 · Answer 12 · 2026-03-25 17:39:44

70

Views

Proving $\sum_{k=0}^{p-1} {k \choose l}$ is divisible by p

Published on 25 Mar 2026 - 17:39

score 152 · Answer 13 · 2018-03-02 18:53:45

152

Views

Why do all residues occur in this similar sequence?

Published on 02 Mar 2018 - 18:53

score 82 · Answer 14 · 2026-03-25 12:54:24

82

Views

Is the set of odd primes a maximal "Anti-ideal"?

Published on 25 Mar 2026 - 12:54

score 213 · Answer 15 · 2026-03-22 23:52:23

213

Views

Can we prove that $p_N + 3 \leq 2 p_{N-1}$ for sufficiently large $N$?

Published on 22 Mar 2026 - 23:52

List Question

Find the upper bound and lower bound of the number of prime numbers less than x

A solution using 'Lifting the exponent' lemma to IMO 1990 P3

Number Theoretic Estimate $\sum_{p\leq y}\frac{\log p}{p}h(pt)=\int_{t}^{yt}\frac{h(v)}{v}\ dv+O\big(h(y)\big)$

Let $\phi$ be Euler's totient function, find all $n$ such that $\phi(n) = \frac{1}{3} n$.

If $p$ is prime, with $p> 3$, then $p^{2} \equiv1\pmod{24}$

Bounding Maximal gaps with Ramanujan primes

Given a sufficiently large integer $N$, is it true that there are more primes than perfect squares in $[1,N]$?

Prove that there are infinitely many primes of the form $6n + 5$

Prove that if $p$ is a prime number, then $p|n^p-n$

$n=2^k-1$ iff ${n \choose 1}, {n \choose 2}, ..., {n \choose n-1}$ are odd

NT Divisibility with Primes

Proving $\sum_{k=0}^{p-1} {k \choose l}$ is divisible by p

Why do all residues occur in this similar sequence?

Is the set of odd primes a maximal "Anti-ideal"?

Can we prove that $p_N + 3 \leq 2 p_{N-1}$ for sufficiently large $N$?

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