Smallest Unknown Prime

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The Smallest Unknown Prime

What is the smallest unknown prime? To put explain what I mean by this question, here is a list of the smallest & largest known & unknown prime numbers.

A prime number is a positive whole number that cannot be divided evenly into smaller parts.

The Smallest Known Prime

Is 2. In Euclid's Elements, Book VII, Definition 11, he says "A prime number is that which is measured by a unit alone." No one knows who discovered the smallest known prime. Whoever first thought of the idea of prime numbers would have immediately figured out a list of the first few primes, and would have discovered that 2 is prime. The number 1 seems to be in the same category, however Euclid considered the number 1 a "unit" rather than a number, so by his definition, 1 is not a prime number. Modern mathematicians also consider 2 to be the first prime. The modern definitions says a prime number is a natural number that has exactly two distinct natural number divisors. See the Wikipedia article on Prime Numbers.

The Largest Unknown Prime

No Answer. There are an infinite number of primes. Euclid proved this.

The Largest Known Prime

Is currently 274,207,281 − 1. This number will keep changing, as we discover larger and larger prime numbers. See Wikipedia's page for the current number.

cooper boone
Curtis Cooper and Steven Boone

The Smallest Unknown Prime

The prime numbers we know about are not in order. The largest known prime is much larger than many prime numbers we don't know about. So the question is, what is the smallest prime number that we don't know? Of course, if we discover the answer to that question, then that number is no longer unknown. It's kind of like the Interesting Number Paradox, or the tomb of the Unknown Soldier.

Maybe a better way to ask the question is this: what's the highest number such that we know whether that number, plus all the ones less than that number, are prime or composite.


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Created and maintained by Matthew Weathers. Last updated February 2, 2017.