While Goldbach’s conjecture is that

*every even number equal to or greater than 4 can be expressed as the sum of two primes*,

**minus-Goldbach’s conjecture**(I call it this way because it’s unnamed but has to be referred to) is that

*every even number can be expressed as the difference between two primes*.

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

**2**

**n**(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

**p**

**1**и

**p**

**2**, 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=**

**│**

**2**

**n**

**│**

**+**

**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__.