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Question Number 503 by 123456 last updated on 20/Jan/15

$$prooforgivenacounter-example:$$$$ifn\in \mathbb{N},n>1,existanumberk\in \mathbb{N}$$$$k\in (0,n]suchthatn+kisprime.$$

Commented by prakash jain last updated on 20/Jan/15

$${\mathrm{Bertrand}}^{\prime }\mathrm{s}\mathrm{theorem}\mathrm{states}\mathrm{that}$$$$\mathrm{if}{p}_i\mathrm{is}{i}^{th}\mathrm{prime}\mathrm{than}{p}_{i+1}<2\cdot p_i$$$$\mathrm{The}\mathrm{statement}\mathrm{given}\mathrm{in}\mathrm{question}$$$$\mathrm{directly}\mathrm{follows}\mathrm{from}\mathrm{Bertrand}\mathrm{theorem}$$$$\mathrm{for}k=p_{i+1}-p_i,\mathrm{where}{p}_i=n.$$

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