Nth Prime Number Calculator

How it is calculated

A prime is a whole number greater than 1 whose only divisors are 1 and itself. To find the n-th prime the tool starts at 2 and checks each following integer by trial division: a number is prime if no integer from 2 up to its square root divides it evenly. Every prime found increases a counter, and the search stops when the counter reaches n. The position n is cut to a whole number and must be between 1 and 20,000; anything outside that range returns no result. Counting starts at 1, so n = 1 gives 2, n = 2 gives 3 and n = 3 gives 5. The result is the prime itself, not its position.

Common mistakes

• Counting 1 as a prime; the first prime is 2.
• Mixing up the position with the value: n = 100 asks for the 100th prime, not whether 100 is prime.
• Using a zero-based index as programmers do; here the first prime is n = 1, not n = 0.
• Entering a number above 20,000, which the tool does not accept.
• Entering a decimal such as 10.7 and expecting rounding; the fraction is simply dropped.