List questions from primorial

Published on 02 Mar 2022 - 21:07

140

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Why is this alternating summation involving reciprocals of divisors always positive? A conjecture.

Published on 04 Mar 2022 - 8:43

91

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Why does the golden ratio emerge in this primorial-related sequence?

Published on 08 Apr 2022 - 9:03

44

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Stuck on reading a proof of $n\# < 4^n$

Published on 20 Apr 2022 - 18:01

55

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Expressing any even natural number as a sum of primorials with coefficients

Published on 24 Feb 2026 - 2:18

45

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Tight lower and upper estimate of alternating summation of reciprocals of divisors of primorial $\sum_{d \mid p_n\#} (-1)^{\omega(d)} \dfrac{1}{d}$?

Published on 12 Jun 2022 - 18:10

120

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Does Chebyshev's theorem provide a lower bound of the primorial $n\#$ such that $n\# \ge 2^{n/2}$

Published on 25 Mar 2026 - 16:46

70

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Does it follow that $\lim\limits_{n \rightarrow \infty} \sqrt[n]{n\#} = e$?

Published on 12 Jul 2022 - 7:00

39

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Reasoning about limits related to the prime number theorem

Published on 12 Jul 2022 - 18:20

38

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$H_{c,n}(y)=\sum_{c\mid d\mid p_n\#}(-1)^{\omega(d)}[\dfrac{y-z_{c,d}}{d}]$ is asymptotic to $\sum_{c\mid d\mid p_n\#}(-1)^{\omega(d)}[\dfrac{y}{d}]$?

Published on 30 Sep 2022 - 3:07

84

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Proving $x*\ln(\ln(x))>\ln(\ln(x\#))$ for $\infty>$x>e$

Published on 22 Oct 2022 - 4:08

32

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Growth of x relative to the Primorials?

Published on 09 Jan 2023 - 22:54

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Related to Problem 4697 from Crux Mathematicorum

Is this old news? $\sum_{i=1}^n \frac{i!}{p_i\#} \approx 1.240053652689\dots$

Why is this alternating summation involving reciprocals of divisors always positive? A conjecture.

Why does the golden ratio emerge in this primorial-related sequence?

Stuck on reading a proof of $n\# < 4^n$

Expressing any even natural number as a sum of primorials with coefficients

Tight lower and upper estimate of alternating summation of reciprocals of divisors of primorial $\sum_{d \mid p_n\#} (-1)^{\omega(d)} \dfrac{1}{d}$?

Does Chebyshev's theorem provide a lower bound of the primorial $n\#$ such that $n\# \ge 2^{n/2}$

Does it follow that $\lim\limits_{n \rightarrow \infty} \sqrt[n]{n\#} = e$?

Reasoning about limits related to the prime number theorem

$H_{c,n}(y)=\sum_{c\mid d\mid p_n\#}(-1)^{\omega(d)}[\dfrac{y-z_{c,d}}{d}]$ is asymptotic to $\sum_{c\mid d\mid p_n\#}(-1)^{\omega(d)}[\dfrac{y}{d}]$?

Proving $x*\ln(\ln(x))>\ln(\ln(x\#))$ for $\infty>$x>e$

Growth of x relative to the Primorials?

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