While for every even number the number of corresponding Goldbach’s pairs is finite, the number of minus-Goldbach’s pairs is not (see how easy one can time-jump 107 years ahead and reach the Polignac's conjecture). In order to have the algorithm stop we have to choose an interval, in which a finite number of pairs is calculated (see Step 3 below).
My algorithm for calculating minus-Goldbach’s pairs is following:
Step 1. Choose 2n (any even number that you want expressed as the difference between two primes).
Step 2. Find │2n│ (absolute value of 2n) and its half │n│.
Step 3. To find the primes p1 и p2, the difference of which is 2n, you have to search for them at a distance of │n│ from the natural number x (x=│2n│+i). The values of i are natural numbers between 1 and z. You must also choose the value of z, which is the maximum remoteness of x from │2n│. Thanks to those limitations we are able to calculate a finite number of pairs of primes, otherwise the algorithm wouldn’t be able to stop (see above).
Step 4. For every i=1 to z, calculate x (x=│2n│+i), p2 (p2=x-│n│) and p1 (p1=x+│n│).
Step 5. If p2 and p1 are primes, i.e. if every time when each is divided by 2 or odd numbers lesser than it (excluding 1) there are remainders existing, then output them.
Thanks to Plamen Antonov, you can see the only 'minus-Golbach' calculator on the web here.