Prime Numbers

If $x, y$ and $z$ are distinct prime numbers, then their LCM is _______

Prove that $n^4+4^n$ is a composite number for all $n\in \mathrm{\mathbb{N}},n>1$.

Prove that there are infinitely many primes.

Two prime numbers $A, B(A<B)$ are called twin primes if they differ by $2 ($e.g. $11,13,$ or $41, 43, ....)$  If $A$ and $B$ are twin primes with $B>23,$ then what is the largest number that would always divide $A+B ?$

$A$ and $B$ are playing mathematical puzzles. $A$ asks $B$ "find the number of whole numbers, greater than one, which can divide all the nine three-digit numbers $111, 222, 333, 444, 555, 666, 777, 888$ and $999.$" $B$ immediately gave the desired answer. What it was ?

What is the maximum possible value of $n$ for which $2013$ can be written as a sum of $n$ consecutive positive integers ?

By which smallest number we should divide $198396198,$ to get a perfect square ?

$\mathrm{p}, \mathrm{q}$ and $\mathrm{r}$ are three prime numbers satisfying the relation $\mathrm{p} + \mathrm{q} = \mathrm{r}$ and $\mathrm{p} < \mathrm{q}$. What is the value of $\mathrm{p}$?

a and b are twin prime numbers satisfy the condition $(6\mathrm{K}\pm 1)$ and another prime number c satisfy the condition $(8\mathrm{K}+1)$. Find the least value of a prime number $\mathrm{p}$ which satisfy the condition ${\mathrm{a}}^2+{\mathrm{b}}^2={\mathrm{c}}^2+{\mathrm{p}}^2$ and $\mathrm{K}$ is a natural number.

A prime number $p$ is called special if there exist primes $p_1, p_2, p_3, p_4$ such that $p=p_1+p_2=p_3-p_4.$
The number of special primes is
 

A two-digit number $\overline{ab}$ is called almost prime if one obtains a two-digit prime number by changing at most one of its digits $a \& b$. (For example, 18 is an almost prime number because 13 is a prime number). Then the number of almost prime two-digit numbers is

Find out the prime factors of $28.$

Find out the prime factors for $49.$

Find the number which is a prime number.

What is prime factorization?

Express each number as the product of its prime factors. Use repeated division method.

$117$

Express each number as the product of its prime factors. Use repeated division method.

$256$

Express each number as the product of its prime factors. Use repeated division method.

$42$

Express each number as the product of its prime factors. Use repeated division method.

$150$

Express each number as the product of its prime factors. Use repeated division method.

$112$