# Tagged Questions

49 views

### Is there a 10-digit emirp?

Does a 10-digit emirp exist? Unfortunately, the lists of emirps I could find on the Web are quite small and my programming skills aren't good enough to write a program to check all the primes up to ...
102 views

### Property of set of prime numbers

let $\{p_1,p_2,p_2,\cdots ,p_r\}$ be the set of $r$($\ge2$) pair wise distinct prime numbers i.e.., $(i\ne j \implies p_i \ne p_j)$ for all $1\le i,j\le r$ ${Statement}$ : For any such ...
33 views

66 views

### What is the well-known result used to prove primality of $n=2pq+1$ under certain conditions?

On Henri Lifchitz's website, we find: If $n=2pq+1$, $p$ and $q$ primes and $q>2p$, if there is an integer $a$ such $a^{n-1} \equiv 1 \pmod n$ and $\gcd(a^{2p}-1,n)=1$ then $n$ is prime. It is ...
46 views

### Have either of these sequences been cataloged?

Let $x(n)$ be the remainder when $p(n + 2)$ is divided by 3, where $p(n)$ is the $n$-th prime. Let $y(n)$ = $x(n)$ - 1. Then $\{y(n)\}$ is a binary sequence, that is, is a sequence of $0$'s and ...
268 views

### Logical consequence of Euclid's theorem

Are there any far reaching non-trivial consequences of Euclid's infinitude of primes where theorems make use of it? Wikipedia does not have the list of applications of this theorem, rather modern ...