Practice question · Multiple choice
Every even number above 2 checked so far is the sum of two primes, verified past 4 × 10¹⁸. Why is Goldbach's conjecture still a conjecture?
Hints
- Compare the number of cases checked with the number remaining.
- Pólya's conjecture held for about 900 million cases. What happened after?
Show the answer
B. Because no finite verification touches an infinite domain
Why
Four quintillion is a rounding error against infinity, and the history is a warning: Pólya's conjecture survived to around 900 million and Skewes' number shows a crossover far past any feasible search. Verification builds confidence and never converts a universal claim, which is the whole reason proof exists.
Practise Direct Proof and Counterexample
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More questions on Direct Proof and Counterexample
- Checking that a claim about all integers holds for the first ten thousand cases is not a proof, while a…
- A claim that holds for the first one million integers is thereby proven for all integers.
- Order the steps of a direct proof that the sum of two even integers is even.
- Claim: 'every prime number is odd'. Select every value that is a genuine COUNTEREXAMPLE.
- Sort each claim by what it would take to settle it.