Big Maths Ideas · Beta

Goldbach’s conjecture

Find prime pairs for an even number and compare examples with a universal claim.

Select an even integer greater than 2, then choose a pair of primes that adds to it.

5+23=285+23=28
Select an even integer greater than 2, then choose a pair of primes that adds to it.5 (prime)23 (prime)028

This even number has 2 prime pairs.

Unordered prime pairs
2
The idea behind the experiment

Goldbach’s conjecture proposes that every even integer greater than 2 is the sum of two primes. It remains unproved. Testing the finite range on this slider cannot establish the claim for every even integer.

Oxford Maths on Goldbach
Predict, test and explain

Step 1 of 3

Predict

How many unordered prime pairs add to 10?

InvestigateHow many unordered prime pairs make 28?

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Try it in the simulation. Change one thing at a time.

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Hints, self-check and connections
Try a self-check

Fixed values, separate from the diagram controls.

How many unordered prime pairs add to 10?

10=p+q,p,q prime10=p+q,\quad p,q\text{ prime}

Hint

A prime has exactly two positive divisors.

Reveal answer

The pairs are 3 + 7 and 5 + 5. Swapping 3 and 7 does not create a new unordered pair.

two unordered pairs\text{two unordered pairs}

Build an explanation

Hint 1

A prime has exactly two positive divisors.

Hint 2

Only check the first prime up to half the even number to avoid duplicates.

Hint 3

A finite set of successful tests cannot prove a universal conjecture.

Worked example

This example uses fixed values, separate from the diagram controls.

Find all unordered prime pairs for 10.

  1. Check primes up to 5: 2, 3, 5.
  2. 10 − 2 = 8 is not prime.
  3. 10 − 3 = 7 and 10 − 5 = 5 are prime.

Answer: 3 + 7 and 5 + 5.

Connect this idea

Watch out: Order does not create a different unordered pair.