Question

Show that the number 1111...11 having 65 digits is not a prime

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Answer 1

Let Z=1111111111…………………….1111( 91 times)

The prime factors of 1111111 =239*4649 , So 1111111 is a composite number

Now our number Z can be written as:

Now 1111111=1+1^1+10^2+10^3+10^5+10^6

Z=1111111 +10^7*(1111111)+10^14*(1111111)+……….+10^84*(1111111)

Z=1111111* ( 1+10^7+10^14+10^21+……………+10^84)

Hence Z=1111111111…………………….1111( 91 times)

= 1111111* ( 1+10^7+10^14+10^21+……………+10^84)

This all proves that 1111111111…………………….1111( 91 times) is composite or non-prime number.

Hence Z can not be proved to be a prime numbers

Thanks for asking question.

Answer 2

Step-by-step explanation:

solution is given in the image