Euler – Coder.si

Verifying Primes

Problem 574

Let be a prime and be two integers with the following properties:

It can be shown that, given these conditions, any sum and any difference has to be a prime number. Thus you can verify that a number is prime by showing that either or for some fulfilling the conditions listed above.

Let be the smallest possible value of in any sum and any difference , that verifies being prime. Examples:
, since .
, since is the associated sum with the smallest possible .
since is the associated difference with the smallest possible .

Let be the sum of for all primes . For example, and .

Find .