maths question bugging me

hi, ive seen this style of question in a lot of past intermediate maths papers (edexcel) just cant think of a solution, would be very greatful if someone could solve....

sophie says for any whole number n, the value of 6n-1 is a always a prime number

sophie is wrong
show an example to show sophie is wrong

thanks very much....

Reply 1

pottageb

n=6

Reply 2

military

but isnt 6(6)-1 36-1= 35 isnt 35 prime?

Reply 3

military

o ***** lol woops no its not. soz im alseep, thanks

Reply 4

Dragonkiller

how about 0 ?

Reply 5

Swayum

Or better yet, any negative integer n.

But the trick to this question is to do the question backwards:

Let 6n - 1 = x

6n - 1 = x
6n = (x+1)

You know that the right hand side must be a multiple of 6 because the left hand side is 6n and n is an integer.

Now all you have to do is pick a non prime number that's 1 less than the multiple of 6. You can list out the multiples of 6:

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90.

Look through the list and see which of those numbers, when you subtract 1 from them, don't give a prime. So 36 is a good example. Then x = 35 or x+1 = 36 (the right hand side).

6n = x + 1
6n = 36
n = 6

Not very useful for this question, but could be for harder ones.

Reply 6

Economist'ist

Minus values, ie n=-1

Reply 7

Economist'ist

you beat me ...

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