Random Prime Number Generator

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What does this tool do?

This tool quickly generates a random prime number between 1 and 100,000. You can click the Get a Random Prime button and this tool keeps on returning a prime between 1 and 100,000.

There are a total of 9,592 prime numbers between 1 and 100,000.

What are Prime Numbers?

Prime numbers are natural numbers greater than 1 that have only two positive divisors: 1 and themselves. In other words, a prime number is a whole number greater than 1 that cannot be formed by multiplying two smaller natural numbers. For example, 2, 3, 5, 7, 11, and 13 are prime numbers because they are only divisible by 1 and themselves.

Some key properties of prime numbers include:

  1. Fundamental Building Blocks: Prime numbers are often referred to as the "building blocks" of the natural numbers because any natural number greater than 1 can be expressed uniquely as a product of prime numbers (up to the order of multiplication).

  2. Infinite: There are infinitely many prime numbers. This was first proved by the ancient Greek mathematician Euclid in his famous "Euclid's theorem."

  3. Distribution: Prime numbers become less frequent as we move further along the number line, but they still occur infinitely often. However, there is no known formula to predict the exact distribution of prime numbers.

  4. Primality Testing: Determining whether a given number is prime is a fundamental problem in number theory. While there are efficient algorithms for primality testing, it becomes computationally difficult for very large numbers.

Prime numbers have applications in various fields such as cryptography, number theory, computer science, and even in everyday life (e.g., in generating secure encryption keys). They are fundamental objects of study in mathematics and have intrigued mathematicians for centuries.