Goldbach’s conjecture

Example · High school

Every even integer greater than $2$ is the sum of two primes.

Terms

Term	This example	Why
conjecture	✓	Goldbach’s conjecture is a conjecture, because it is a mathematical statement that is believed true but has no proof.
theorem	✗	Goldbach’s conjecture is not a theorem, because it has not been proved.
hypothesis (in science)	✗	Goldbach’s conjecture is not a hypothesis, because checking more even numbers cannot establish it; only a proof can.

Distinctions using this example

• Conjecture vs. hypothesis vs. law vs. theory

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