Prove that there is an even integer n such that n 30 and n

Prove that there is an even integer n such that n > 30 and n can be written as the sum of two prime numbers.

Solution

Let D be a even number greater than 30.

D=A+B+C+...+n such that where no of elements in the equation is a odd number and where A,B,C are prime numbers and D is even number.

Now according to Goldbach\'s conjecture every even number greater than 2 can indeed be written as the sum of two primes.

so our D can be written as sum of two primes.