Question

The number of 10 digit numbers such that the product of any two consecutive digits in the number is a prime number is

Answer 1

The total possible number is 2048.

Step-by-step explanation:

Given : The number of 10 digit numbers such that the product of any two consecutive digits in the number is a prime number.

To find : The number is ?

Solution :

Case 1 :

Consider |x| |x| |x| |x| |x| where x=1,2,3,4,5 or 7.

For each section we have 4 possible selections [2,3,5,7]

So, we multiply 4, 5 times

i.e. $4\times 4\times 4\times 4\times 4=4^5=2^{10}$

Case 2 :

Consider |x| |x| |x| |x| |x| where x=2,3,5,7

For each section we have 4 possible selections [2,3,5,7]

So, we multiply 4, 5 times

i.e. $4\times 4\times 4\times 4\times 4=4^5=2^{10}$

The total possible numbers are $2^{10}+2^{10}$

$2\times 2^{10}=2^{11}=2048$

Therefore, the total possible number is 2048.

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Answer 2

The total possible number is 2048.

Step-by-step explanation:

Given : The number of 10 digit numbers such that the product of any two consecutive digits in the number is a prime number.

To find : The number is ?

Solution :

Case 1 :

Consider |x| |x| |x| |x| |x| where x=1,2,3,4,5 or 7.

For each section we have 4 possible selections [2,3,5,7]

So, we multiply 4, 5 times

i.e.

Case 2 :

Consider |x| |x| |x| |x| |x| where x=2,3,5,7

For each section we have 4 possible selections [2,3,5,7]

So, we multiply 4, 5 times

i.e.

The total possible numbers are

Therefore, the total possible number is 2048.