Question Number 223801 by wewji12 last updated on 05/Aug/25
$$\mathrm{sorry}\:\:\mathrm{i}\:\mathrm{mean}\:{p}_{{h}} \in\mathbb{P}\:\left(\mathrm{prime}\:\mathrm{set}\right) \\ $$$$\underset{{h}\rightarrow\infty} {\mathrm{lim}}\:\frac{{p}_{{h}+\mathrm{1}} }{{p}_{{h}} }=?? \\ $$
Commented by Ghisom last updated on 05/Aug/25
$$\mathrm{we}\:\mathrm{know}\:\mathrm{the}\:\mathrm{gaps}\:\mathrm{between}\:\mathrm{primes}\:\mathrm{are} \\ $$$$\mathrm{getting}\:\mathrm{larger}\:\overset{?} {\Rightarrow}\:\frac{{p}_{{h}+\mathrm{1}} }{{p}_{{h}} }\:\rightarrow+\infty \\ $$$$\mathrm{but}\:\mathrm{we}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{there}\:\mathrm{are}\:\mathrm{infinite}\:\mathrm{twin} \\ $$$$\mathrm{primes}\:\left({p}_{{k}} ,\:{q}_{{k}} ={p}_{{k}} +\mathrm{2}\right).\:\mathrm{if}\:\mathrm{so},\:\frac{{q}_{{k}} }{{p}_{{k}} }\:\rightarrow\:\mathrm{1} \\ $$$$\Rightarrow \\ $$$$\mathrm{we}\:\mathrm{cannot}\:\mathrm{answer}\:\mathrm{the}\:\mathrm{question} \\ $$