Question

help needed!
Are all primes (past 2 and 3) of the forms 6n+1 and 6n-1?

Answer 1

yuppppp

Answer 2

u dereee

Answer 3

any kind of proof?

Answer 4

i dk that

Answer 5

ok....take any integer n greater than 3, and divide it by 6. That is, write
n = 6q + r, where q is a non-negative integer and the remainder r is one of 0, 1, 2, 3, 4, or 5.
so, If the remainder is 0, 2 or 4, then the number n is divisible by 2, and can not be prime.
Also, If the remainder is 3, then the number n is divisible by 3, and can not be prime.

Answer 6

so...by this we can say that... if n is prime, then the remainder r is either
--->1 (and n = 6q + 1 is one more than a multiple of six), or
--->5 (and n = 6q + 5 = 6(q+1) - 1 is one less than a multiple of six).

Answer 7

Is that a proof?

Answer 8

yeah!! remember that being one more or less than a multiple of six does not make a number prime. We have only shown that all primes other than 2 and 3 (which divide 6) have this form....
Hope it helps!

Answer 9

yes i can get it..

Answer 10

division algorithm guarantees that you can represent EVERY number in the form `6q+r` where `0<=r<6`

Answer 11

so proving for those 6 cases is like proving for every integer

Answer 12

oh! well. Anyways thanks a ton @aryandecoolest @ganeshie8

Answer 13

counterexample

for 6n+1
49
for 6n-1
35

Answer 14

thanks @ikram002p . I understood

Answer 15

:) np