All Primes?

Number Theory Level 2

Which of the below statements is/are true ?

A $\Rightarrow$ All numbers of the form $6n\pm1$ are prime(where ‘n’ is a positive integer).

B $\Rightarrow$ All primes(except 2 and 3) are of the form $6n\pm1$

Only A Only B Both A and B Neither A nor B

1 solution

Theodore Sinclair
May 17, 2018

A is clearly not true as when n=4, 6n+1 will be a multiple of 5 (it ends in a 5).

However, apart from 2 all primes are odd and can either be of the form 6n+1, 6n+3 or 6n-1. However, except for 3 no 6n+3 number can be prime as they all divide by 3.

What about 91 = 6(15)+ 1
91 is divisible by 13

Rahul Sharma - 3 years ago

Not all numbers of the form $6n\pm1$ are prime but all primes must be of the form $6n\pm1$

Theodore Sinclair - 3 years ago

All Primes?

1 solution

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