Question Number 510 by 123456 last updated on 21/Jan/15
$${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$ $${if}\:{p},{q}\:{are}\:{prines}\:{with}\:{p}>{q},\:{and}\:\exists{s}\:{prime} \\ $$ $${such}\:{s}\in\left({q},{p}\right)\:{then} \\ $$ $${p}−{q}\leqslant\underset{{r}\in\left({q},{p}\right),{r}\:{is}\:{prime}} {\sum}{r} \\ $$ $$ \\ $$
Commented byprakash jain last updated on 22/Jan/15
$$\mathrm{Finding}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\:\mathrm{will} \\ $$ $$\mathrm{need}\:\mathrm{three}\:\mathrm{consecutive}\:\mathrm{primes} \\ $$ $${q},\:{s},\:{p}\:\mathrm{such}\:\mathrm{that} \\ $$ $${s}={q}+{k} \\ $$ $${p}>\mathrm{2}{q}+{k} \\ $$ $$ \\ $$