List questions from prime-numbers

Published on 20 May 2014 - 20:20

300

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Proof of Infinite Primes in the form $10^{\lceil k \log_{10}(n) \rceil }+n^{k-1}$

Published on 21 May 2014 - 4:45

4k

Views

How do we prove $p_n\sim n\log(n\log(n))$ from the Prime Number Theorem?

Published on 02 Apr 2026 - 3:48

821

Views

$n$th prime & prime number theorem

Published on 21 May 2014 - 11:22

449

Views

Finding an integer (if one exists) $n$ such that $n$, $n+1$, $n+2$, $n+3$, $n+4$ are all composite

Published on 25 Mar 2026 - 13:55

81

Views

$n$th prime bounded from above?

Published on 21 May 2014 - 15:05

83

Views

Show $x^{\pi(x)} < 3^x$ using the PNT.

Published on 21 May 2014 - 16:23

213

Views

Using Bertrand's Postulate

Published on 21 May 2014 - 19:22

1.9k

Views

Finding smallest and largest prime factor of $\frac{200!}{180!}$

Published on 27 Mar 2026 - 15:36

127

Views

$\pi(x)\leq \frac x{f(x)}$ for some unbounded function $f(x)$

Published on 02 Apr 2026 - 3:48

409

Views

Existence of a prime partition

Published on 26 Mar 2026 - 9:40

815

Views

How to prove if an arithmetic function is multiplicative?

Published on 25 Mar 2026 - 9:25

2.2k

Views

Decimal form of irrational numbers

Published on 22 May 2014 - 13:43

87

Views

Is my proof correct regarding the non primality of $2\cdot 17^a +1$?

Published on 22 May 2014 - 15:07

487

Views

Show that $\mathbb{Q}(\zeta)$ contains one of the two numbers $\sqrt{\pm5}$ and decide which one is contained in $\mathbb{Q}(\zeta)$.

Published on 25 Mar 2026 - 23:42

List Question

Sum of Residues Modulo $p^2$.

Proof of Infinite Primes in the form $10^{\lceil k \log_{10}(n) \rceil }+n^{k-1}$

How do we prove $p_n\sim n\log(n\log(n))$ from the Prime Number Theorem?

$n$th prime & prime number theorem

Finding an integer (if one exists) $n$ such that $n$, $n+1$, $n+2$, $n+3$, $n+4$ are all composite

$n$th prime bounded from above?

Show $x^{\pi(x)} < 3^x$ using the PNT.

Using Bertrand's Postulate

Finding smallest and largest prime factor of $\frac{200!}{180!}$

$\pi(x)\leq \frac x{f(x)}$ for some unbounded function $f(x)$

Existence of a prime partition

How to prove if an arithmetic function is multiplicative?

Decimal form of irrational numbers

Is my proof correct regarding the non primality of $2\cdot 17^a +1$?

Show that $\mathbb{Q}(\zeta)$ contains one of the two numbers $\sqrt{\pm5}$ and decide which one is contained in $\mathbb{Q}(\zeta)$.

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