In class, we talked about the Twin Prime Conjecture, which stated that there were infinitely many primes p such that p+2 is also prime. This conjecture hasn't been proven, even though it is believed to be true. Has anyone wondered how close together these primes are? Or if there is a function that would give us these twin primes? On http://primes.utm.edu/top20/page.php?id=1 I found a function that estimates the number of twin primes less than a given number. Even though this isn't an exact function, the results seem to be accurate with known information! For example, the function estimates that there are 27411417 twin primes less than 10^10. The actual value has been determine to be 27412679, which is a difference of only 000046%. I wonder how accurate this formula remains when even larger values are considered?

Twin Primes