Pop quiz: what’s a prime number? Easy. This is any number that has only two factors — be it 1 and that number itself. You got that right, huh? You’re a genius, aren’t you? But wait until you solve this simple math problem. Numbers are infinite, and so are prime numbers, and certain prime numbers have a unique feature. For instance, 11 and 13 have a difference of 2, and so is 599 and 601, too. Such prime numbers are said to be a “twin prime.” Now, is it infinitely possible that there are infinitely many twin primes? If yes, then prove it!
Related media: Finding Twin Prime And The Twin Prime Conjecture
Twin Prime Conjecture
The Twin Prime Conjecture is the most famous of all number theories — the mathematical study of natural numbers and their properties, but frequently involving prime numbers. Proving this simple theory has ever since its inception proven impossible. Now, let’s take you a bit in detail. For all observations, the first in a pair of twin primes is always 1 less than a multiple of 6 — with one exception, though. And the second twin prime is always 1 more than a multiple of 6. Confused? Get ready for some mind-blowing number theory.
All prime numbers after 2 are odd, and even numbers are always 0, 2, or 4 more than a multiple of 6, whereas odd numbers are always 1, 3, or 5 more than a multiple of 6. Here’s the catch: one of those three possibilities for odd numbers causes an issue. If a number is 3 more than a multiple of 6, then that number has to be a factor of 3. But having a factor of 3 means a number isn’t prime (with the only exception being 3 itself). And that’s simply why every third odd number can’t be prime.
Why Art Thou A Problem?
Millennia ago, the ancient Greek mathematician Euclid proved that prime numbers themselves are infinite, and this leaves the possibility that twin primes might do so, too. But this isn’t prove, though it seems obvious. But come on, is there any proof? Not at all. For now, all mathematicians can testify is that there’s an infinite number of prime numbers differing by not more than 246 — and it seems here’s where it begins.
However, the good news is, mathematicians have managed to solve quite a similar problem related to this problem, and this was there solution. If there’s always a problem proving that there are infinitely many prime numbers with a difference of 2; what about a problem trying to prove that there are infinitely many prime numbers with a difference of, say 70,000,000? There isn’t. This was cleverly proven in 2013 by mathematician Yitang Zhang at the University of New Hampshire.
Twin Aren’t Forever
And ever since, mathematicians have been trying to improving Zhang’s proof from the millions right down to the hundreds; and its just a matter of time and brilliance for someone to take it down all the way to 2 and there will be the solution to the Twin Prime Conjecture. But the closest we’ve gotten to is 6 — though there are a few technical assumptions, and reducing 6 to 2 is the most seemingly simplest math problem in the universe.
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Written by: Nana Kwadwo, Thu, Oct 28, 2021.