Unproven hypotheses about prime numbers

Although people have a lot of knowledge about prime numbers, there are still many hypotheses that cannot be proved or rejected, such as the hypothesis of two twin prime numbers or hypothetical primes.

According to Business Insider, prime numbers are numbers that can only be divisible by 1 and itself. All other natural numbers can represent the performance of prime numbers, for example 12 = 2 x 2 x 3; 50 = 5 x 5 x 2; 69 = 3 x 23. Ancient mathematician Euclid once had a famous proof of the infinite number of primes.

Here are the hypotheses that cannot be proved or disproved about prime numbers.

Twin prime numbers

Two twin prime numbers are a pair of prime numbers separated by exactly one number on the natural number line, for example 5 and 7, 11 and 13, 29 and 31 . Hypothesis of prime numbers Sometimes, there is an infinite number of such pairs.

Although many mathematicians think this hypothesis is true. Although the prime numbers are rarer as the numbers grow, the experience and intuition of arithmetic theorists suggests that twin pairs of prime numbers will still appear. However, this hypothesis is not really proven or rejected.

In the spring of 2013, the University of New Hampshire mathematician Yitang Zhang invented a new technique that proved that there were numerous pairs of primes in which there were no more than 70 million other numbers in between.

Although this is still a huge number, but for the first time a finite limit on the number of primes ever discovered, can be considered a breakthrough in the process of proving the hypothesis.

Then, in the fall of 2013, a group of mathematicians added to Zhang's work and showed shorter and shorter distances. In the end, they proved that there were innumerable number of prime pairs with only 246 other numbers alternating between.

The most famous downward primes, or demonic primes.(Photo: ILUK).

Goldback hypothesis

This is a simple hypothesis that the Prussian mathematician lived in the 16th century, Goldback gave: every even number greater than 2 can be expressed as the sum of two primes, for example 4 = 2 + 2, 8 = 5 + 3, 20 = 13 + 7. However, it has not been proven to all even numbers.

Researchers in the 21st century with the help of computers and modern calculation programs have verified this hypothesis for even numbers to the limit of 4 billion (4 and 18 0). However in mathematics, this still does not mean that the hypothesis is true for all even numbers.

The number of primes is reversed

Reverse primes are prime numbers that remain the same whether reading from left to right or right to left. Examples 11, 101, 16561. The most famous reverse prime is number 10000000000066600000000000001: number 1 is 13, 0 is followed by 666, then 13 and 0 ends. show Satan demon in the Bible. The number of 13 0s is also a number that is considered bad. This can be considered the most unfortunate prime factor.

Similar to twin prime pairs, it is still not possible to determine whether the number of forward and reverse primes is infinite. It is also less used in mathematics than twin primes.

The difference between the two types is that a number of elements have a reverse nature that is not entirely dependent on the counting system: the reverse primes in the binary are completely different in the decimal system. Example No. 31 does not reverse in the decimal system, but in binary it is 1111, which has a reverse nature. However, no matter which counting system is used, mathematicians still conclude that the reverse primes are very rare in the set of reverse numbers.

Riemann hypothesis

This is one of the millennium problems, the collection of the most important open problems in mathematics. Resolving any of these issues is up to a million USD.

The Riemann hypothesis (after the 19th century German mathematician Bernhard Riemann) provides a much more accurate estimate of the number of prime numbers smaller than a given number. However, like these hypotheses, although it has been proven to be true for billions of cases, it has not been proved to be universal.