Prime Model

Introduction to prime model:

In this article we shall discuss about prime model. Here, prime model is also denoted as prime number model. A Prime Number is a complete number, bigger than 1, so as to can be uniformly divided just by 1 otherwise itself. "Prime Factorization" is recognized which prime numbers need to multiply as one to get the original number.

Here, few prime numbers are:  1, 7, 13, and 19 etc...

The prime factorization model of a number is multiplying prime factors of a number.

Here, simple example is 38 = 2 x 19.

Examples of Prime Number Model:

The example of 1 - 100 prime number model is shown given below that,

Prime number of 1 - 10:

The prime number of 1 - 10 is 2, 3, 5 and 7.

Prime number of 10 - 20:

The prime number of 10 - 20 is 11, 13, 17 and 19.

Prime number of 20 - 30:

The prime number of 20 - 30 is 23 and 29.

Prime number of 30 - 40:

The prime number of 30 - 40 is 31 and 37.

Prime number of 40 - 50:

The prime number of 40 - 50 is 41, 43 and 47.

Prime number of 50 - 60:

The prime number of 50 - 60 is 53 and 59.

Prime number of 60 - 70:

The prime number of 60 - 70 is 61 and 67.

Prime number of 70 - 80:

The prime number of 70 - 80 is 71, 73 and 79.

Prime number of 80 - 90:

The prime number of 80 - 90 is 83 and 89.

Prime number of 90 - 100:

The prime number of 90 - 100 is 97. Please express your views of this topic Perfect Number by commenting on blog.

Example Problems Based on Prime Factorization Model:

Example problems based on prime factorization model is given below that,

Example:

How to find prime factorization model for 78?

Solution:

Step 1:

To create through the smallest amount prime number, which is 2, then the value is

`78/2 = 39`

Step 2:

Here 39 is not a prime number, therefore we require factoring it over again:

`39/3 = 13`

Step 3:

13 is a prime number,

78 = 13 × 3 × 2. This is the answer; all factors are a prime number. Since a result should be Correct.

Step 4:

The prime factorization for 78 is 13 × 3 × 2.

Prime Number Greater Than

Introduction to Prime Numbers

Prime numbers are those numbers that cannot be divided by any other number other than 1 and the number itself without leaving a remainder. This means prime numbers have exactly two divisors the number itself and one.

Examples: 2,3,5,7,11,13,17,19 etc .

To explain this further let us take 17. Number 17 cannot be divided by any other number other than 17 or 1. If we divide 17 by any other number, there will be a reminder or 17 can be expressed only in one form

17 = 17 x 1

Consider number 18. This number 18 can be divided by 1, 2, 3,6 and 9 without leaving a reminder. Hence, 18 is not a prime number. Numbers that are not prime numbers are called composite numbers. 18 is a composite number and can be expressed in many forms like

18 = 1 x 18

18=  2 x 9

18= 3 x 6 etc

Note: Number 1 is considered as neither prime nor composite

Method to Find Prime Numbers

Now we will see how to find prime numbers greater than a particular number. Here, we must note that there is no fixed method of solving this. We need to find out whether the number can be divided by another number other than the number and one. However, a few thumb rules can of help to identify the numbers fast:

Rule 1: All even numbers are composite numbers except 2. If we find a number to be even other than 2 then it cannot be a prime number as it is divided by 2
Rule 2: If the sum of the digits of the number is divisible by 3 then the number itself is divisible by 3 and it is not a prime number. Exception is number 3 itself. Number 3 is a prime number. This rule checks for the divisibility of three.
Rule 3: If the number ends with 5, it is not a prime number. Exception is number 5. Number 5 is a prime number. This rule checks for the divisibility of 5.
Rule 4: If the sum of the odd digits of the number when subtracted from the even digits of the number gives a number divisible by 11 or 0 then the number is divisible by 11 and is not a prime number. Exception is number 11. Number 11 is a prime number.
Ex: Consider number 14641.

Sol: Step 1: The sum of the numbers at odd places is 1+6+1 = 8

Step 2: Sum of the numbers at the even places is 4+4 =8

Step 3: Difference of the sum of the digits at odd and even places is 8-8 =0

Step 4: Hence, the number 14641 is divisible by 11 and is not a prime number.

Let us try some examples

Ex 1: Identify the prime numbers form the list

42, 57,83,75,98

Sol:   Step 1: 42 and 98 are even numbers hence are not prime

Step 2: Sum of the digits of 57 is 5+7=12 is divisible by 3.

Hence, the number is divisible by 3 and is not a prime number

Step 3: 75 – Ends with 5 and is divisible by 5 and hence not a prime number

Step 4: 83 – is the prime number in the list

Ex 2: Find the first prime number greater than 109?

Sol: This example can only be solved with a few trial and errors and with intelligent guesses. Let us check some of the numbers after 109. We can eliminate all odd numbers as they cannot be prime numbers.

Step 1: 111- This is divisible by 3 as the sum of the digits is 3

Step 2: 113 – This could be a prime number

Step 3: 115 –  This number ends with 5 and not a prime number

Step 4: The maximum possible divisor of a number is half the number. This means that a number can never be divided by a number greater than half its value. So for 113, we need to check whether any number less than 66 can divide the number.

Step 5: 113 cannot be divided by any number divisible by 2, 3 or 5 as 113 itself is not divisible by these numbers. This means that we should check whether 113 is divisible by other prime numbers like 7, 11,13,17,19,23,29,31, 37,41,43,47,53,59 and 61.Since, it is not divisible by any of these numbers, it is a prime number.

Checking whether a number is prime or not goes by the method of elimination. If the divisibility rules are used and if any of the divisors are found then it is definitely not a prime number. But if the number is big and you are not able to identify any divisors using the divisibility rules we CANNOT conclude that it is a prime number. It can have any higher prime number as divisor

For example 588139 is not divisible by 2,3, 5 or 11 etc. But we can write it as below

588139 = 839 x 701 and hence 588139 is NOT a prime number.

Here, 839 and 701 are prime numbers and hence identifying them as divisors manually will be difficult. However, the process can be carried out easily using soft wares.

Between, if you have problem on these topics adding rational expressions with different denominators, please browse expert math related websites for more help on help with math online.

Exercises on Prime Numbers.
Pro 1: Write the first five prime numbers greater than 100.

Ans: 101, 103, 107, 109 and 113

Pro 2: identify the prime number from the following

568, 965, 983, 1353

Ans: 983

Pro 3: Find the first prime number greater than 856

Ans: 857