Consecutive Numbers and Alternate Numbers

Here we will learn about the consecutive numbers and alternate numbers.

Natural numbers come consecutively whereas odd or even numbers come alternatively.

Consecutive Numbers:

Natural numbers which differ by 1 are called consecutive numbers.

For example: 1, 2, 3, 4, 5, 6, 7, etc. are consecutive numbers.


Alternate Numbers:

Numbers which differ by 2 are called alternate numbers.

For example: 1,3,5,7, etc. are alternate numbers.


Solved examples 

1. Write seven consecutive composite numbers less than 100, such that there is no prime number in between them.

Solution:

Seven such consecutive composite numbers are

                              90, 91, 92, 93, 94, 95, 96.


2. Write all the alternate numbers less than 25.

Solution:

21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1


3. Find two consecutive composition numbers less than 10, such that there is no prime number between them.

Solution:

First find the composite numbers less than 10.

4, 6, 8 and 9 are the composite numbers less than 10.

Now we need to check the all consecutive pairs;

(i) 4 and 6

5 is the prime number between 4 and 6.


(ii) 6 and 8

7 is the prime number between 6 and 8.


(iii) 8 and 9

There is no prime number between 8 and 9, so this pair satisfies the condition.

Answer: 8 and 9 


3. The number 137 is a three-digit number which remains prime number whichever way we arrange its digits. Find other such three-digit prime numbers having the same characteristics.

Solution:

137 is a three-digit number which remains prime number whichever way we arrange its digits.

Let's check

173 is a prime number prime, since there are no common factors other than 1 and 173.

317 is a prime number prime, since there are no common factors other than 1 and 317 .

371 is a prime number prime, since there are no common factors other than 1 and 371 .

713 is a prime number prime, since there are no common factors other than 1 and 713.

731 is a prime number prime, since there are no common factors other than 1 and 731.

Now we have to find three such different three-digit prime numbers which remains prime number whichever way we arrange its digits.

(i) 139

(ii) 199

(iii) 237

The above three numbers are such different three-digit prime numbers which remains prime number whichever way we arrange its digits.

Answer: 139; 199; 237

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