) Does there exist a sequence of 10^100 consecutive composite numbers?

Question

Question

math Advanced-Math

Answer 1

Answer #1

Yes , there exist a sequence of composite numbers.

Let = 10^ 100

t is possible to have N consecutive composite numbers. The series -

(N+2)!+2,(N+2)!+3, (N+2)!+4,......., (N+2)!+(N+2)

It is easy to prove it because, N! is a multiplication of all numbers from 1 to N, so you can see

(N+2)!+2(N+2)!+2 will give you 2 as common factor

(N+2)!+3(N+2)!+3 will give you 3 as common factor

.

(N+2)!+(N+2)(N+2)!+(N+2) will give you (N+2) as common factor

showing N consecutive composite numbers.

Answer 2

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