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Algebra

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12 Nov 2008 13:05:57 IST

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Strictly for <11th Please

None

(a) Prove that the sum of two consecutive primes can never be twice a prime(b) Also post the time required by you to get at the solution (No, I am dead serious!)

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Rahul Duggal

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12 Nov 2008 15:27:50 IST

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Re:Strictly for <11th Please

Hari Shankar

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12 Nov 2008 15:59:16 IST

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I wanted to title this one as just for laughs gags!

It had my mind in a spin for about 5 mins as i wondered how to represent consecutive primes, then wondered if some modular analysis would work, till it struck me to do what rahul did.

You've got to admit, I gave you a scare. Am I right?

Tiger on prowl.......

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12 Nov 2008 16:03:57 IST

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observe that a prime can be of form 6k+1 and 6k-1.consecutive primes must be of this form.

if we add them,we get 12k which is twice that of a muliple of 6.

it took me a minute!!!!!!!!!(to be modest)

Tiger on prowl.......

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12 Nov 2008 16:04:54 IST

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sorry........i did not see the title for <11th...............bhat sir,i am really sorry.........

Hari Shankar

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12 Nov 2008 19:46:50 IST

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@satwik:If you had written 6k₁+1 and 6k₂-1 perhaps you wouldnt have committed the error of adding 'em up to get 12k

Tiger on prowl.......

Blazing goIITian

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12 Nov 2008 20:02:06 IST

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sir i can write 6k-1 and 6k+1 because twin primes are of this form(3,5 an exception) for some k.

can you tell me where i went wrong?

Hari Shankar

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12 Nov 2008 20:10:13 IST

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Oh! but see I mentioned consecutive primes not twin primes. e.g. 13 and 17. again 23 and 29 (both 6k-1).

edit: also 31,37 both 6k+1

Tiger on prowl.......

Blazing goIITian

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12 Nov 2008 20:18:25 IST

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ok thank you sir,i understood the flaw............

gauravtargetsiit

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12 Nov 2008 20:24:41 IST

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let p, q and r be three primes such that p and q are consecutive

now according to problem p+ q = 2r

or (p+ q) /2 = r

therefore r lies between p and q

but since p and q are consecutive primes (as assumed) , therefore r cannot be a prime

I took about 3 minutes

Madmax

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12 Nov 2008 21:51:36 IST

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I figured out the same way tht Rahul N Gaurav did

took me about a minute to do so...but I'm not <11th so....

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