What is the mathematical formula to find the sum of the first 1000 prime numbers? I am trying to improve my coding skills at codeeval (doing practice problems).
One of the programming questions I have to answer is to write code that will sum the first 1000 prime numbers.
What is the mathematical formula to find the sum of the first 1000 prime numbers?

I can think of it in terms of an algorithm, not essentially a formula. 
A very interesting way to do so is the Sieve of Erathosthenes, and its algorithm looks like the following: 
Input: an integer n > 1

Let A be an array of Boolean values, indexed by integers 2 to n,
initially all set to true.

for i = 2, 3, 4, ..., √n :
  if A[i] is true:
    for j = i2, i2+i, i2+2i, ..., n:
      A[j] := false

Now all i such that A[i] is true are prime.

