0
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.
Still curious? Ask our experts.
Chat with our AI personalities
Maxine
Vivi
ProfessorAdd your answer:
Earn +20 pts
What did euclid do for math?
euclid wanted to prove that things were true by using logic and reason.
What is the connection between Euclid and prime numbers?
Euclid (c. 300 BC) was one of the first to prove that there are infinitely many prime numbers. His proof was essentially to assume that there were a finite number of prime numbers, and arrive at a contradiction. Thus, there must be infinitely many prime numbers. Specifically, he supposed that if there were a finite number of prime numbers, then if one were to multiply all those prime numbers together and add 1, it would result in a number that was not divisible by any of the (finite number of) prime numbers, thus would itself be a prime number larger than the largest prime number in the assumed list - a contradiction.
Who was euclid and why was he interested in how many prime numbers exist?
Euclid was a Greek mathematician, and is called the father of geometry. A prime number is any number that can only be divided by itself and one. There are an infinite number of prime numbers. As a mathematician Euclid was interested the pursuit of knowledge for knowledge's sake and in proving that things could be quantified (how many, how much). In the case of primes the answer of "there are an infinitely large number of primes" was not available to him as the Greeks did not have the concept of "infinite".
What is the largest prime factor of 42?
The largest prime factor of 42 is 7
What is the largest prime no lesser than 1000?
The largest prime number less than 1000 is 997.The largest prime number no less than 1000 is currently 257,885,161-1
