1eh?
isn't that too easy?
See for any prime > 2 all primes are odd So twin primes will always be consecutive odd numbers. The number between them will always be even and hence will be divisible by 2 . :)
1.Prove that the number between a pair of twin prime numbers is always divisible by 2.
Twin prime numbers are prime numbers whose difference is 2.
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341To build up on this:
Prove that for any prime p we cannot find twin primes p_1, p_2 such that p_1+p_2=2p
21let p_{1}=p_{2}+2
so, 2p2+2=2p
or,p2+1=p
therefore p2 and p are consecutive primes..........
2 and 3 may be the sol.................
but 2*3≠2+4
or, 2*2≠3+5
so no sol.
341also p = p1+p22 would be a prime lying between p1 and p2 which is absurd as p1 and p2 are consecutive primes
39Something interesting to build up ont he question
take this as part 2 of the question
see this first: http://mathworld.wolfram.com/PrimePairs.html
Pairs of primes separated by a single number are called prime pairs. Example: 17,19.
Here's the quetsion:
Prove that the number between prime pair is always divisible by 6 (assuming both numbers are greater than 6)
11Sorry for the mistake.
It should be divisible by 6.
And Nasiko has just answered it