If K is a prime is there a prime between k and 2k. Obviously this is a weaker version of a prime between n and 2n that was proved by Erdos and Chebyshev. Lets assume that their isn't a prime between k and 2k. This would imply that all the numbers between k and 2k would have to be constructed from primes smaller than K. When I say constructed I mean their prime factorization. so there would have to be some product of primes that was in between k and 2k , [itex] k<P_1P_2....P_n<2k [/itex] with [itex] P_n<K [/itex] ok so as soon as we had one number in between k and 2k then the smallest prime that we could multiply it by is 2, but 2 times this product of primes would be bigger than 2k so we would not have constructed all the numbers between k and 2k. Actually I thought I could arrive at a contradiction but I lost my train of thought. any help would be much appreciated.