Did Euclid Prove There Are Infinitely Many Prime Numbers?

💡 The Answer

• Euclid's proof from around 300 BC is a classic example of proof by contradiction.
• He assumed a finite list of primes, then constructed a number not divisible by any.
• That number must either be prime itself or have a prime factor not in the list.
• This contradiction shows the list cannot be complete, proving infinitude.