Mistrz Witold

# THE MYSTERY IN NUMBER THEORY – PRIME NUMBERS

When It comes to a subject like math, we are expected to know everything about it. But that is not necessarily true. Prime Numbers is a centralized topic in mathematics. However much about prime numbers remains as a mind-boggling mystery. Prime numbers are considered to be one of the most basic of issues in the Number Theory branch. Prime numbers are merely numbers that can be evenly divided by themselves the number 1. Prime numbers are known to be the building blocks of natural numbers, which makes it one of the most critical topics in Number theory. Studying or following a maths career includes the study of prime numbers. This study has led to many discoveries about prime numbers. One of the most famous inventions is that there is an infinite amount of primary numbers. A simple strategy proved this discovery if prime numbers were finite and were listed, then multiplying them and adding one will create a new unlisted prime number. This proof would completely contradict the idea of having a limited amount of prime numbers, making it completely infinite. Even though we know much about prime numbers, many concepts are still shrouded in mystery and are still unproven. Some of these concepts are listed below;

• Twin Primes
• Goldbach’s Conjecture
• Palindromic Primes
• The Reiman Hypothesis

## Twin Primes

These are numbers that are separated by only one number, i.e., 11 and 13, and 5 and 7. This conjecture suggests that are an infinite number of Twin Primes among the Prime numbers. While several researchers and mathematicians believe that the theory to be true, there is an excellent debate about it. As the value of numbers increase, the twin primes also begin to show up often. However, the conjecture has not been proved neither has it been disproved right up to 2013. Springtime of the year was the year that made it for leading mathematician Yitang Zhang. The theory which was never proved finally had a solution. He was able to suggest with enough evidence that the conjecture was, in fact, true. However, the number of pairs are limited to 70,000,000. While the number is substantial in itself, we at least have a definite number to work with. ## Goldbach’s Conjectures

This conjecture says that any number that is larger than two can be derived from summing up to prime numbers. While it is right for many single instances, the theory has not proved to work for all prime numbers. With computer programming techniques this theory has been confirmed that all even numbers are a sum of two prime number – A case that was unproven up to a point.

## Palindromic Primes These are numbers that read the same when they are read both forward and backward like the number 101. The number of palindromic primes has not been established till date. However, researchers over time have been able to firmly suggest that palindromic primes are a rare occurrence and that not all palindromes are primes.

## The Riemann Hypothesis

The hypothesis is one of the problems that carry a reward of \$1 million if solved correctly. The Nobel prize-winning problem involves the number of primes smaller than a given large number through a formula. A full-blown proof of the working of this formula is yet to be unearthed entirely and is an obsessive math problem that scientists have been hoping to crack for decades. The solving of the hypothesis will provide new avenues of research and insights into several areas.