Question Number 196638 by mr W last updated on 28/Aug/23
$${find}\:{the}\:{sum}\:{of}\:{the}\:{all}\:\mathrm{168}\:{prime} \\ $$$${numbers}\:{from}\:\mathrm{1}\:{to}\:\mathrm{1000}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{13245} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{52788} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{76127} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{86344} \\ $$
Commented by mahdipoor last updated on 28/Aug/23
$$\mathrm{I}\rangle\Sigma=\left(\mathrm{2}\right)+\left({sum}\:{of}\:\mathrm{167}\:{p}.{n}\:{that}\:{are}\:{odd}\right)={odd} \\ $$$$\mathrm{II}\rangle\mathrm{1}+\mathrm{2}+…+\mathrm{168}<\mathrm{2}+\mathrm{3}+\mathrm{7}+…+\left(\mathrm{168}'{th}\:{p}.{n}\right) \\ $$$$\Rightarrow\mathrm{14196}<\Sigma \\ $$$$\left.\mathrm{I}\:\&\:\mathrm{II}\:\Rightarrow\:\mathrm{3}\right)\:\Rightarrow\:\mathrm{76127} \\ $$
Commented by mr W last updated on 28/Aug/23
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Commented by AST last updated on 28/Aug/23
$$\mathrm{1}\:{even}\:{prime}+\mathrm{167}{odd}\:{prime}\Rightarrow{sum}\:{is}\:{odd} \\ $$$${Sum}\:{of}\:{first}\:\mathrm{168}\:{prime}\:{numbers}>{Sum}\:{of}\:{first} \\ $$$$\mathrm{168}\:{even}\:{integers}\Rightarrow{Answer}>\mathrm{2}\left(\frac{\mathrm{167}×\mathrm{168}}{\mathrm{2}}\right)=\mathrm{28392} \\ $$$$\left.\Rightarrow\mathrm{3}\right) \\ $$