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What are the prime numbers ? and what are their definition, characteristics, facts and properties

In this article, we will learn what are prime numbers, what are their

 definition, what are their  characteristics, what are the most important prime numbers, and is zero a prime number or not. We will

 know all of that or more on the mathematics page in English



?What is the definition of prime numbers

The definition of primes is the positive integers greater than the first

 number, which can be divided into only two numbers, which are the

 same number and the other without a remainder. Like the numbers

 13 and 17, as for the positive integers greater than one, which accept

 division by another number, which is a group called complex

 numbers, they are numbers that can be divided, such as the number

 28, which has several factors, and it must be pointed out here that

 the two numbers (0 , 1) they are always excluded from two lists: the

 prime and complex numbers, while the number (2) is the smallest

 prime number, which is the only prime even number.

?What are the properties of the prime numbers

  • All primes except (2) are odd.
  • All integers greater than (3) can be expressed as a result of the sum of two prime numbers.
  • Only the first consecutive spouses (2,3).
  • All integers are (0,1), either as prime numbers or complex numbers
  • No number can end with one of the two numbers (0, 5); Like 25, 30 is a prime number.
  • If the sum of the numbers consisting of multiples of the number (3) then this number cannot be prime.

?How to determine the prime numbers
    • The complex number is distinguished by the fact that it accepts division by a prime number less than or equal to its root without a remainder. If the number (n) is complex, then it must accept division without remaining on one of the prime numbers less than or equal to n Remaining on all these numbers, this means that the number is prime;
    For example, the number 23 cannot be divided by any prime number less than or equal to 23√ without a remainder, and this proves that it is prime.
    • To factorize; Through this method, it is possible to determine if the number is prime in a simple and fast manner, and summarize it by searching for
      . If we take the number 15 as an example, then we find that 3 and 5 multiplied by 15, and therefore the number 15 is considered a complex and not prime. Because there are other numbers that he can divide by without a remainder, which are:

    Illustrative examples of the initial numbers

    One of the most important initial numbers 

    2, 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53.73.79,83,89,97,101,103,107,109
    113,127,131,137,139,149,151,179,181,191,193,197,199,211,223,227,229,233
    227,229,233,239,241,251,257,263,283.293.307.311.313.317.331.337.347

     Illustrative examples of no preliminary counter



    Why are the following numbers preliminary (73, 79, 83, 89) are prime numbers    1. 

    Solve a problem: all of these numbers can be divided by the

     correct one without remainder and the same number

     2. What are the primes between (178 and 198)

    Solve a math problem: the numbers between the following two

     numbers are 179, 181, 191,193, 193, 197

    3. Are the following numbers primary or not primary

     (compound) (13, 15, 18, 23, 200, 251)

    problem solution:

    • The number 13 is a  because it is divisible by one without a remainder and it is divisible by itself
    • The number 15 is not prime (complex)  because it is a result of multiplying 3 x 5, so it can be divided by   3, 5 
    • The number 18 is not prime (complex)  because it is a result of multiplying 2 x 9 or 3 x 6, so it can be divided by 2, resulting in 9 or vice versa, and it can be divided by 3, resulting in 5 or vice versa
    • The number 23 is a  because it is divisible by one without a remainder and it is divisible by itself
    • The number 200 is not prime (complex)  because it is a result of multiplying 2 x 100 or 20 x 10.
    • The number 251 is a  because it is divisible by one without a remainder and it is divisible by itself

    Analysis of numbers to their elementary elements

    How can the following numbers be analyzed into their

     elementary elements (12, 30)

    Solving a math problem: analysis of number 12
    • 12 is a product of 2 x 6
    • 2 is prime
    • 6 is the product of 2 x 3, which are prime
    • The prime numbers for 12 are 2 x 2 x 3
    The solution: analyze issue 30
    • 30 is 2 x 15
    • 2 is prime
    • 15 is a product of 3 x 5, which are two prime numbers
    • The prime numbers for the number 30 are 2 x 3 x 5

    Is zero a prime number

    Zero is not a prime number but rather one of the most

     important real numbers








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