New posts in prime-numbers

A conjecture about the prime function $p_n$: $p_m \cdot p_n >p_{m \cdot n}$

Accuracy of approximation to inclusion-exclusion formula in prime sieve

Prove at least two are not relatively prime, for any $8$ composite positive integers not exceeding $360$

Is there any number greater than 8 of the form $2^{2k+1}$ which is the sum of a prime and a safe prime?

Do 4 consecutive primes always form a polygon?

Is either $n! + 1$ or $n! - 1$ not prime for all $n$?

Why in Sieve of Erastothenes of $N$ number you need to check and cross out numbers up to $\sqrt{N}$? How it's proved?

Why does $\phi(pq)=\phi(p)\phi(q)$?

Connections between prime numbers and geometry

How to prove indirectly that if $42^n - 1$ is prime then n is odd?

Are Hilbert primes also Hilbert irreducible ? Furthermore, are Hilbert primes also primes in $\mathbb{ Z}$?

Why can no prime number appear as the length of a hypotenuse in more than one Pythagorean triangle?

Find all the prime factors of $1000027$

Multiplying prime numbers

how to prove that $1^x+2^x+3^x+4^x+\cdots+N^x$ will never sum to a prime number except $1^x+2^x$?

The use of log in the Mean density of the nontrivial zeros of the Riemann zeta function (part 2)

How can I prove analytically the number $2^{100000}+1$ is not prime??

Proof by Contradiction - two distinct primes not divisible by each other

does a number that contains all primes less than it exist?

Is the sum of two distinct primes an injective function on integers?