Practice question · True or false
A claim that holds for the first one million integers is thereby proven for all integers.
Hints
- Consider how many integers remain unchecked after a million.
- Recall the polynomial that produced 40 primes before failing.
Show the answer
False
Why
False. A million confirmations leave infinitely many cases untested. Polya's conjecture survived far beyond a million before failing, and Euler's polynomial gave 40 primes before breaking, evidence is not proof.
Practise Direct Proof and Counterexample
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