How many prime numbers are there between 50 and 100?

To verify the number of primes in this range, we must first recall the definition of a prime number: a whole number greater than 1 that cannot be formed by multiplying two smaller whole numbers. In other words, its only factors are 1 and itself. To find the primes between 50 and 100, we can systematically test each number. We immediately eliminate all even numbers and numbers ending in 5. For the remaining numbers, like 51 or 57, we check for divisibility by smaller primes (51 is 3 x 17, and 57 is 3 x 19). The numbers that survive this filtering process are 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97, giving us a total of ten.

This count highlights an important concept in number theory known as the Prime Number Theorem, which describes the distribution of primes. As numbers get larger, prime numbers become less common. For comparison, there are 15 primes between 1 and 50, but only 10 in the next fifty numbers. Despite this thinning out, the Greek mathematician Euclid famously proved around 300 BC that there is an infinite number of primes, so they never run out. Today, the hunt (Review) for massive, previously unknown prime numbers continues with the help of supercomputers, as they are essential for modern data encryption.