# Is this a prime number??

• Apr 25th 2011, 05:10 AM
bryan06
Is this a prime number??
Is (3^9 -1)/2 prime??I'll also need to justify my answer using the method along the lines of group theory or mod but have no idea :S thxxxxx
• Apr 25th 2011, 05:15 AM
alexmahone
Quote:

Originally Posted by bryan06
Is (3^9 -1)/2 prime??I'll also need to justify my answer using the method along the lines of group theory or mod but have no idea :S thxxxxx

(3^9-1)/2=[(3^3)3-1^3]/2=(3^3-1)(3^6+3^3+1)/2=[(3^3-1)/2]*(3^6+3^3+1)

Note that both factors are natural numbers. So, (3^9-1)/2 is not prime.
• Apr 25th 2011, 08:03 AM
bryan06
thank you so much for your reply, much appreciated~~~but im so sorry i am kind of lost already wen i try to understand (3^9-1)/2=[(3^3)3-1^3]/2...do you actually mean that or is there a typo??or have i mis-read something?the number involved in the question is (3^9 -1)/2 which is 9841, just in case there's any notation error. would you be very kind and explain briefly your working pleaseee?? thankssssss

Quote:

Originally Posted by alexmahone
(3^9-1)/2=[(3^3)3-1^3]/2=(3^3-1)(3^6+3^3+1)/2=[(3^3-1)/2]*(3^6+3^3+1)

Note that both factors are natural numbers. So, (3^9-1)/2 is not prime.

• Apr 25th 2011, 08:03 AM
CaptainBlack
Quote:

Originally Posted by bryan06
Is (3^9 -1)/2 prime??I'll also need to justify my answer using the method along the lines of group theory or mod but have no idea :S thxxxxx

No, since it is less than 10000 you need only check for divisibility by odd primes less than 100 and there are only 24 of those and you can rule out 3 and 5 straight off. Now proving it by some other method is another question, maybe the Lucas–Lehmer test would do (but it still looks more complicated than trial division by the primes less than 100)

CB
• Apr 25th 2011, 08:11 AM
alexmahone
Quote:

Originally Posted by bryan06
thank you so much for your reply, much appreciated~~~but im so sorry i am kind of lost already wen i try to understand (3^9-1)/2=[(3^3)3-1^3]/2...do you actually mean that or is there a typo??or have i mis-read something?the number involved in the question is (3^9 -1)/2 which is 9841, just in case there's any notation error. would you be very kind and explain briefly your working pleaseee?? thankssssss

I merely factorised the given number (9841=13x757).

-------------------------------------------------------------

3^9=(3^3)^3
1=1^3

I then used the "difference of cubes" formula.
• Apr 25th 2011, 08:14 AM
bryan06
ahhhh i see i see thank you soo much :)

Quote:

Originally Posted by alexmahone
I merely factorised the given number (9841=13x757).

-------------------------------------------------------------

3^9=(3^3)^3
1=1^3

I then used the "difference of cubes" formula.

• Apr 25th 2011, 08:18 AM
bryan06
but what happens if we're not allowed a calculator (like in my exam)??becoz then we would never know the number is 9841 and therefore cannot use this method. is there another method possible??perhaps using "mod"?? :S
• Apr 25th 2011, 08:20 AM
alexmahone
Quote:

Originally Posted by bryan06
but what happens if we're not allowed a calculator (like in my exam)??becoz then we would never know the number is 9841 and therefore cannot use this method. is there another method possible??perhaps using "mod"?? :S

I didn't use a calculator when I wrote post #2...
• Apr 25th 2011, 09:17 AM
bryan06
so you mean there was no need to know the number was 9841 in the first place??or did u work it out by hand?? cheers :)

Quote:

Originally Posted by alexmahone
I didn't use a calculator when I wrote post #2...

• Apr 25th 2011, 09:19 AM
alexmahone
Quote:

Originally Posted by bryan06
so you mean there was no need to know the number was 9841 in the first place??

Exactly.

Quote:

Originally Posted by bryan06
or did u work it out by hand??

Nope.
• Apr 25th 2011, 09:24 AM
bryan06
i get it now :) thx :D
Quote:

Originally Posted by alexmahone
Exactly.

Nope.