A prime number is a number that cannot be divided by other number apart from itself and the number 1. Here is a list of the prime numbers below one hundred: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Two consecutive prime numbers are called twin primes when they differ one from another by just two units. If you have a look to the list of primes above, you will realize that the first pairs of twin primes are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).

Since the great Euclid (around 300 BC) we know that there are infinitely many prime numbers. But, are there infinitely many twin primes?

Mathematicians believe that the answer is yes, but nobody has been able to prove this conjecture yet.

Note that the only even prime is 2, so twin primes are as closely spaced as possible for two primes –with a gap distance of 2–, except for the pair (2, 3) with a gap distance of 1. In April 2013, Yitang Zhang announced the discover that there are infinitely many pairs of primes that differ by a gap of some number below 70000000 approximately. Nowadays, the math comunity is trying to reduce this large gap of 70 million to just 2 units.

 

References:

https://en.wikipedia.org/wiki/Twin_prime

http://www.macfound.org/fellows/927/

http://mathground.net/another-unsolved-problem-polignacs-conjecture/

 

 

  • Guest - M4TES

    April '15: James Maynard and a collaboration group have just shown for certain that there are infinitely many pairs of primes that differ by at most 246. This number is quite closer to the number 2 of the twin primes conjecture than the first result involving the number 70,000,000. The conjecture about twin primes is likely to become a theorem soon! (We hope).

    More details at: https://plus.maths.org/content/find-gap

    Comment last edited on about 1 year ago by Super User
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  • Guest - jimmi

    nice

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