Prime Number Calculator

The natural numbers with only two divisors are called the primes. The largest known prime is 2^82589933 - 1 discovered on December 21, 2018. This is a Mersenne prime of the form M_p = 2^p - 1.

The calculator returns either a list of primes up to the limit input by the user or checks to see whether the number input is prime.

The limit is based solely on your patience. A limit of 1,000,000 takes about a second to calculate. But scrolling through the list of 78,498 primes takes significantly longer.

An interesting prime generating equation is the following: $$f\left(n\right)=n^2-n+41$$ For all $n\le {10}^6$ 22% of all $f\left(n\right)$ are prime. The second input box will calculate these primes up to the specified limit.

A limit of 100,000 takes about 40 seconds to calculate as many of the primes found by the equation are quite large, e.g. the largest: 9,999,100,061.

Of interest is the following prime, 357686312646216567629137. It is the longest left-truncatable prime: you always get a prime no matter how many leading digits you remove.