Intereting Posts

Find the equation of the polar
$f$ not differentiable at $(0,0)$ but all directional derivatives exist
How many ways are there to define sine and cosine?
Efficient Method to find funsum$(n) \pmod m$ where funsum$(n)= 0^0 + 1^1 + 2^2 + … n^n$
$\Bbb Z_m \times \Bbb Z_n$ isomorphic to $\Bbb Z_{\operatorname{lcm}(m,n)}\times \Bbb Z_{\gcd(m,n)}$
Multivariate function interpolation
Stirling-like sum equal to zero when $k>n$
Proving two lines trisects a line
Find $N$ when $N(N – 101)$ is the square of a positive integer
Is any closed ball non-compact in an infinite dimensional space?
Integral $\int_0^{\infty} \frac{\ln \cos^2 x}{x^2}dx=-\pi$
Is the negation of the Gödel sentence always unprovable too?
Show a subspace formed by a Klein bottle is homotopy-equivalent to $S^1 \vee S^1 \vee S^2$
Proof of an elliptic equation.
Proving that the terms of the sequence $(nx-\lfloor nx \rfloor)$ is dense in $$.

Related.

Show that if $x$ is large enough,$$\prod_{\substack{p<x \\ p \ \text{prime}}}\frac{1}{p^{N+1}-1}>\frac{0.2}{\log^2 x}.$$

Speaking of which, Theorem 6.12, and maybe others, of this paper might be useful.

If $N$ cannot be arbitrarily large for the inequality to hold, any conditions for truthfulness regarding its value are welcome.

- Asymptotics for Mertens function
- Show that $(n!)^{(n-1)!}$ divides $(n!)!$
- Asymptotic Distribution of Prime Gaps in Residue Classes
- A triangular representation for the divisor summatory function, $D(x)$
- Fermat: Prove $a^4-b^4=c^2$ impossible
- Decomposition as a product of factors

- Three pythagorean triples
- Are Euclid numbers squarefree?
- Weierstrass factorization theorem and primality function
- What are some examples of theories stronger than Presburger Arithmetic but weaker than Peano Arithmetic?
- special values of zeta function and L-functions
- For what $t$ does $\lim\limits_{n \to \infty} \frac{1}{n^t} \sum\limits_{k=1}^n \text{prime}(k)$ converge?
- Is there any real number except 1 which is equal to its own irrationality measure?
- Suppose $p, p+2, p+4$ are prime numbers. Prove that $p = 3$ not using division algorithm.
- number of ordered partitions of integer
- Finding $n$ satisfying that there is no set $(a,b,c,d)$ such that $a^2+b^2=c^2$ and $a^2+nb^2=d^2$

Your inequality is equivalent to $$-\underset{p\leq x}{\sum}\log\left(p^{N+1}-1\right)>\log\left(0.2\right)-2\log\left(\log\left(x\right)\right).$$

Now we have, for partial summation and Prime Number Theorem, that exists $c_{1},c_{2}>0$

such that $$-\log\left(0.2\right)-\underset{p\leq x}{\sum}\log\left(p^{N+1}-1\right)<-\underset{p\leq x}{\sum}\log\left(p\right)=-\left(c_{1}x+c_{2}\frac{x}{\log\left(x\right)}+o\left(\frac{x}{\log\left(x\right)}\right)\right)<-cx<-2\log\left(\log\left(x\right)\right)$$

for some $c>0$

and $x$

large enough. So it is false.

- Proof that the symmetric difference is associative
- Reference for the subgroup structure of $PSL(2,q)$
- How to prove that this solution of heat equation is not a tempered distribution?
- Heat equation asymptotic behaviour 2
- What's the Maclaurin Series of $f(x)=\frac{1}{(1-x)^2}$?
- Trig substitution for a triple integral
- An explicit construction for an everywhere discontinuous real function with $F((a+b)/2)\leq(F(a)+F(b))/2$?
- Prove: $a_n \leq b_n \implies \limsup a_n \leq \limsup b_n$
- Prove $1^2+2^2+\cdots+n^2 = {n+1\choose2}+2{n+1\choose3}$
- Sum identity using Stirling numbers of the second kind
- How to obtain the equation of the projection/shadow of an ellipsoid into 2D plane?
- Help with proof of Jensens inequality
- Let $a,b,c\in \Bbb R^+$ such that $(1+a+b+c)(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=16$. Find $(a+b+c)$
- Two exercises on characters on Marcus (part 1)
- Show a locally integrable function vanishes almost everywhere