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Question Number 160109 by abdullah_ff last updated on 24/Nov/21

How many numbers are there which  contain 5 digits and the sum and   product of the digits are both prime  numbers?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{there}\:\mathrm{which} \\ $$$$\mathrm{contain}\:\mathrm{5}\:\mathrm{digits}\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{and}\: \\ $$$$\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{both}\:\mathrm{prime} \\ $$$$\mathrm{numbers}? \\ $$

Commented by abdullah_ff last updated on 25/Nov/21

thanX Sir

$${than}\mathcal{X}\:\mathbb{S}\mathrm{ir} \\ $$

Commented by MJS_new last updated on 24/Nov/21

5 digits and the product is prime  11112 11121 11211 12111 21111 sum=6  11113 ... sum=7 ★  11115 ... sum=9  11117 ... sum=11 ★  ⇒ 10 numbers

$$\mathrm{5}\:\mathrm{digits}\:\mathrm{and}\:\mathrm{the}\:\mathrm{product}\:\mathrm{is}\:\mathrm{prime} \\ $$$$\mathrm{11112}\:\mathrm{11121}\:\mathrm{11211}\:\mathrm{12111}\:\mathrm{21111}\:\mathrm{sum}=\mathrm{6} \\ $$$$\mathrm{11113}\:...\:\mathrm{sum}=\mathrm{7}\:\bigstar \\ $$$$\mathrm{11115}\:...\:\mathrm{sum}=\mathrm{9} \\ $$$$\mathrm{11117}\:...\:\mathrm{sum}=\mathrm{11}\:\bigstar \\ $$$$\Rightarrow\:\mathrm{10}\:\mathrm{numbers} \\ $$

Commented by Kunal12588 last updated on 24/Nov/21

11113 11117 11131 11171 11311 11711 13111 17111 31111 71111 counter: 10 [Program finished]

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