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How did Euclid prove there is no largest prime?
The proof that there is no largest prime:Assume that there are a finite number of primes for the sake of contradiction. Then, there should be a number P that equals p1p2p3...pn+1. P is either prime or not prime (composite). If it is prime, we just show that P is larger than the largest prime in the list. If it's not prime, it must be composite. Composite always has at least one factor that is prime, but since P is not divisible by any prime in the list, the unknown prime factor(s) must be something not in the list, this also shows that there is a prime larger than the largest prime in the list. Both cases show that no matter how large a list of prime numbers, there will be always at least one larger prime outside of that list.
List all of the prime numbers that are between 20 and 30?
23 29.
List of prime numbers from 75 to 100?
79 83 89 97.
List all of the prime numbers between 20 and 30?
They are 23 and 29.
List the factors of 31 in numerical order?
1, 31 (31 is a prime!)
