If K is a prime is there a prime between k and 2k.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Proof about a prime between k and 2k.

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