Question

Make a list of seven consecutive composite numbers that are less than 100 so that there is no prime number between them.

Answer 1

Hint: We solve this problem by taking all the prime numbers that are less than 100.
We know that there are 25 prime numbers that are less than 100.
We take all the numbers and search for the two consecutive prime numbers having a difference of 8. Because we are asked to find the 7 consecutive composite numbers where there will be no prime number.
So, if two prime numbers have a difference of 8 then there will be 7 numbers between them which are composite numbers.

Complete step by step answer:
We are asked to find the 7 consecutive numbers that are less than 100 where no prime number is present.
We know that there is a total of 25 prime numbers less than 100.
Now, let us make a list of prime numbers that lie between 1 and 10 then we get 2, 3, 5, 7
Now, let us make a list of prime numbers that lie between 10 and 20 then we get 11, 13, 17, 19
Now, let us make a list of prime numbers that lie between 20 and 30 then we get 23, 29
Now, let us make a list of prime numbers that lie between 30 and 40 then we get 31, 37
Now, let us make a list of prime numbers that lie between 40 and 50 then we get 41, 43, 47
Now, let us make a list of prime numbers that lie between 50 and 60 then we get 53, 59
Now, let us make a list of prime numbers that lie between 60 and 70 then we get 61, 67
Now, let us make a list of prime numbers that lie between 70 and 80 then we get 71, 73, 79
Now, let us make a list of prime numbers that lie between 80 and 90 then we get 83, 89
Now, let us make a list of prime numbers that lie between 90 and 100 then we get 97
Now, let us check the two consecutive prime numbers having the difference as 8.
Here, from the list of all prime numbers, we can say that 89 and 97 are the only two consecutive prime numbers that is having a difference of 8
Now, let us list out all the numbers that lie between 89 and 90 then we get 90, 91, 92, 93, 94, 95, 96
Therefore, we can conclude that the list of 7 consecutive composite numbers in which no prime number is present is 90, 91, 92, 93, 94, 95, 96

Note:
In this solution we can see that we listed out all the prime numbers that are less than 100.
Students may so mistake in avoiding some of the prime numbers from the list of 25 prime numbers.
It is very easy to remember the prime numbers because all the prime numbers will be odd numbers except 2 the only even prime number.
So, we can take all the odd numbers less than 100 and check its divisibility with the numbers less than that number.
If it has a factor other than 1and itself then we can say that it is a composite number.
So, remembering the prime numbers less than 100 is a basic property.