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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.
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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".
How many prime numbers are between 0-100?
100
What are all the prime numbers between 15 and 30?
The prime numbers between 15 and 30 are: 17 19 23 29.
How many prime numbers are there between 1-1000?
1001
What is the sum of all prime numbers between 60 and 75?
The sum of all prime numbers between 60 and 75 is 272
