Goldbach Pair Calculator

How it is calculated

The tool takes an even number n and tests each candidate p from 2 up to n / 2. For each one it checks by trial division whether both p and n − p are prime, and stops at the first success. It therefore returns the pair with the smallest first prime, listed as smaller prime and larger prime, and the two always add up to n. Only one pair is shown, even when several exist. The input must be a whole even number of at least 4 and no larger than 2⁵³; odd numbers, decimals, negatives, 2 and anything above that limit return no result. For n = 4 the answer is 2 + 2, and for n = 6 it is 3 + 3. Large results are printed with thousands separators, for example 999,983.

Common mistakes

• Entering an odd number such as 51. The conjecture is about even numbers, so odd input returns no result.
• Entering 2 or a negative number. The smallest accepted value is 4, because 2 cannot be split into two primes.
• Expecting every possible pair. The tool shows only the pair with the smallest prime: for 50 that is 3 + 47, not 19 + 31.
• Treating the result as a proof of the conjecture. A pair for one number says nothing about all even numbers; the conjecture remains unproven.
• Counting 1 as a prime. It is not, so 1 + (n − 1) is never accepted as a pair.