Twin prime conjecture

The twin prime conjecture is a mathematical theory. It says that it is possible to find two twin primes that are as big as wanted.

Twin primes are prime numbers that differ by two. For example, 3 and 5 are both prime and differ by two. They are twin primes. 23 is prime, but it is not a twin prime. The primes nearest to 23 are 19 and 29. Twin primes were discovered by Euclid in 300 B.C.

Since Euclid's time mathematicians have wondered whether there are an infinite number of twin primes. Many mathematicians are still trying to find the answer.

Here is Lawrence Abas' (Aurora Ontario Canada) proposed simple proof of infinite twin primes previously published on Linked-In with no current disputes.

This negative proof considers that a largest-twin-prime pair can only exist if there are a finite number of primes, which creates a paradox.

If there were a finite number of primes, the maximum twin prime would be easy to calculate the result of multiplying that set of primes (call it a prime factorial) plus one or minus one. This this would produce two new numbers that cannot be in that set or have factors that are in that set. Since this makes new prime numbers that are not in the set or composite numbers that have factors that are not in that set a paradox exists.

Consider a set of unique prime numbers where each element is multiplied together. The result minus one, and result plus one cannot be an element in that set. Example: (2,3,5, 7) 2 x 3 x 5 x 7 = 210 210-1=209, 210+1=211. 209 is 11x19 and 211 is prime. 11, 19, and 211 are primes that are not in the set (2,3,5,7)

Since we know from Euclid that an infinite number of primes exist, the maximum twin primes is on n x (the result of all prime numbers multiplied, which is infinity) plus one and minus one. Where n is a natural number from 1 to infinity.

Any natural number multiplied by infinity is infinity, and infinity plus or minus one is still infinity. Therefore, the largest twin prime is infinite.

This negative proof is essentially identical to Euclid's proof of infinite primes except that +1 is changed to +1 and -1.