Smallest Unknown Prime Number

A prime number is a natural number that has exactly two distinct divisors. Like 5939. It’s divisible only by 1 and by 5939. Mathematicians are constantly trying to find bigger and bigger prime numbers. Currently (as of April 2007), the largest know prime number is 232,582,657−1, found last September.

So that’s the largest known prime.

What about the smallest known prime? Or the largest unknown and smallest unknown primes?

The smallest known prime is easy, it’s 2. This was discovered as soon as prime numbers were discovered.

As for the largest unknown prime – this question was settled in around 300 BC by Euclid when he proved there are an infinite number of primes. So there is no answer.

But what about the smallest unknown prime number? That’s an interesting question. Prime numbers are not discovered in order. So it’s smaller than the largest known prime. Also, if you were to come up with the answer, it would immediately not be the answer, because you would know it.

It’s like asking where the list ends. Mathematicians have lists of prime numbers that are complete up to a point. After that point, there are scattered numbers that we know to be prime.

(This is an adaptation of

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