Write a program to print twin primes less than $1000.$ If two consecutive odd numbers are both prime then they are known as twin primes.

Write a program to implement these formulae of permutations and combinations. Number of permutations of $n$ objects taken $r$ at a time: $p(n,r)=\frac{n!}{n-r}!.$

The number of combinations of $n$ objects taken $r$ at a time is: $c(n,r)=\frac{n!}{r{!}^{**}(n-r)!}=p\frac{n,r}{r}!$

$3.$ Write a program to find out the prime factors of a number. Example: prime factors of $56-2,2,2,7$

$4.$ Write a program to implement these formulae of permutations and combinations.

$5.$ Write a function that converts a decimal number to a binary number

$6.$ Write a function cubesum$()$ that accepts an integer and returns the sum of the cubes of individual digits of that number. Use this function to make functions PrintArmstrong$()$ and isArmstrong$()$ to print Armstrong numbers and to find whether is an Armstrong number.

$7.$ Write a function sumPdivisors$()$ that finds the sum of proper divisors of a number. Proper divisors of a number are those numbers by which the number is divisible, except the number itself. For example, proper divisors of $36$ are $1,2,3,4,6,9,18$

$8.$ A number is called perfect if the sum of proper divisors of that number is equal to the number. For example, $28$ is a perfect number, since $1+2+4+7+14=28.$ Write a program to print all the perfect numbers in a given range

$9.$ Two different numbers are called amicable numbers if the sum of the proper divisors of each is equal to the other number. For example, $220$ and $284$ are amicable numbers.

Sum $of$ proper divisors $of220=1+2+4+5+10+11+20+22+44+55+110=284$

Sum $of$ proper divisors $of284=1+2+4+71+142=220$

Write a function to print pairs of amicable numbers in a range