There are an infinite number of prime numbers twins, the difference between them does not exceed 70 million






The author of this important discovery - Associate Professor of the University of New Hampshire Ethan Zhang 50-odd years - before that was virtually unknown to date. This is a rare case in the history of science where breakthrough of this magnitude, as well as the first serious scientific work, scientists published over forty years.




"Twins" in mathematics is called a pair of prime numbers, the difference between them is 2 (eg, 11 and 13). A "simple" is the number that are divisible only by themselves and by one, in contrast to the composite numbers.

In the middle of the XIX century mathematician Alphonse de Polignac noticed a strange pattern associated with the distribution of prime numbers in the natural number. The numbers above, the less the number of across-the twins. De Polignac was convinced that the number of twin numbers indefinitely. But so far nobody has been able to either prove this hypothesis, nor deny.

Many have tried to find evidence with the help of the so-called method of "sieve" -that is, filtering out the numbers which are divided into simple divider - 2, 3, 5, 7, and so on. D. The first pair is easy to find - 3 and 5; 5 and 7; 11 and 13; 17 and 19, and so on. However, more is becoming more difficult. To date, the largest known to science twin pair of numbers - is 3756801695685 and 3756801695685 × 2666669-1 × 2666669 +1.




In 2005, the year of mathematics Dan Goldston of the University of San Jose (California) and colleagues Who Yildirim and Janos Pinzi developed a method by which failed to prove that the distance between the prime numbers, regardless of their size has certain limits. However, it is outside, they find out it was not possible.

Zhang puzzled over this mystery for many years. It has developed a set of new mathematical methods that, in the end, and allowed him to solve one of the oldest mathematical problems.

Initially, the work obscure mathematics without titles and regalia, sent to the journal Annals of Mathematics, was adopted by the mathematical community is skeptical. However, after several mathematicians found her evidence given in perfect name Ethan Zheng thundered to the whole world.

via factroom.ru

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