Mathematics

An Introduction to Prime Numbers



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What is a prime number? The prime number in mathematics is a base number. What is a base number? It is a number that serves as a "base" or "foundation" to be built up from. What does this mean? It means it is a natural number. It can only be divisible by itself and "1." It means that it cannot be broken down without some sort of fraction or percentage.

Overall, these numbers cannot be broken down into whole numbers. They would be your "foundation" numbers. All the prime numbers are odd except for "2." "2" is the only even prime number. After that, the prime numbers are as follows: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, and so forth. The prime numbers will get larger and larger. While the prime numbers continue to get bigger, they cannot be reduced into whole numbers. That would mean those big prime numbers are very big foundation numbers. On top of that, the amount of prime numbers is infinite. It means as the numbers get larger, we will come across much larger prime numbers. That would mean the current largest prime number would eventually get replaced by another and larger prime number.

If and when that happens, there is going to be in the news outlets. It will definitely rock the world of mathematics and sciences for awhile. Then, it will fade out until another new larger prime number is discovered. That will be the current largest building block number to be multiplied into a larger number. That prime number will only be divisible by itself or by "1." It shows the interesting thing about numbers, they are infinite. When you are looking at numbers, it is like a never ending story. In a sense, you are reading a mathematical story that never ends. Prime numbers are by no means any different to that concept.

Also keep in mind that "1" is not a prime number. One needs to know that just because a number is odd does not necessarily mean it is a prime number. There are plenty of odd numbers that can be reduced. Remember, a number that cannot be reduced is a prime number.

One could ask: How do you find prime numbers? There are several ways to do this. The first one is pretty simple. It is called the "Sieve of Eratosthenes." It is quite simple as a means to find prime numbers. Under this method, an algorithm is used to find prime numbers below "120." If you are looking for something above "120," you will have to find another method.

Another method is known as the "primality" test. However, this does not necessarily produce prime numbers. You have to input the number yourself. But, you will have to depend on a method called "integer factorization."

Current formulas are Dirichlet's Theorem on Arithmetic Progressions, the Green-Tao Theorem, Diophantine Equations, Mill's Formula, Wilson's Theorem, and Recurrence Relation. Other than that, there are no other known formulas to produce prime numbers.

Today, the largest known prime is "12,978,189." This is the forty-sixth Mersenne Prime. This prime number was discovered in 2008. It was the same year that the forty-fifth Mersenne Prime was discovered. That number was "11,185,272."

Overall, prime numbers are your "base numbers." They cannot be broken down into whole numbers. If you try to break down a prime number, you are going to end up with fractions. That is all right if you are working with fractions. Other than that, these are the numbers you leave alone as they serve as your foundation.

One could compare a prime number to the foundation of a building. In sociology, a prime number could be compared to the primal state of a living being. With that respect, the growing list of prime numbers could be compared to the evolution from a primitive state of mind. Remember, these numbers are only divisible by themselves and "1." It is important to know that "1" is not a prime number.

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