Orally

Number Theory Level 3

Which of the following statement is false?

There exist 1000 consecutive natural numbers none of which is prime none of these given a natural number m m ,there exist m m consecutive natural numbers none of which is prime There exist 100 consecutive natural numbers none of which is prime

Shivam Jadhav by Shivam Jadhav , 22, India

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1 solution

( x + 1 ) ! + 2 , ( x + 1 ) ! + 3 , ⋯ , ( x + 1 ) ! + x , ( x + 1 ) ! + ( x + 1 ) (x+1)!+2,(x+1)!+3, \cdots ,(x+1)!+x , (x+1)!+(x+1)

All these numbers are composite.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Yes , had the same trick in mind :)

Nihar Mahajan - 5 years, 4 months ago

3 ! + 1 = 6 + 1 = 7 3! + 1 = 6 + 1 = 7 is prime

Siddhartha Srivastava - 5 years, 4 months ago

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7 7 is a prime number!

Nihar Mahajan - 5 years, 4 months ago

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I was going to write "not composite", but wrote " Not prime" instead. :/ Edited.

Anyways, it doesn't change my point. x ! + 1 x! + 1 is not always composite.

Siddhartha Srivastava - 5 years, 4 months ago

Fixed.Thanks.

Harsh Shrivastava - 5 years, 4 months ago

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