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Question Number 46045 by Tawa1 last updated on 20/Oct/18
A number is said to be ′′right prime′′ if despite dropping the left most  digits successively,  Number continues to be a prime number.    For example:  223 is a right prime because despite dropping 2 from left  most part, we obtain  23 as the prime number. Next, even after dropping   2 from left,  3 is a prime.       How many two digit numbers are right prime ?
$$\mathrm{A}\:\mathrm{number}\:\mathrm{is}\:\mathrm{said}\:\mathrm{to}\:\mathrm{be}\:''\mathrm{right}\:\mathrm{prime}''\:\mathrm{if}\:\mathrm{despite}\:\mathrm{dropping}\:\mathrm{the}\:\mathrm{left}\:\mathrm{most} \\ $$$$\mathrm{digits}\:\mathrm{successively},\:\:\mathrm{Number}\:\mathrm{continues}\:\mathrm{to}\:\mathrm{be}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}.\:\: \\ $$$$\mathrm{For}\:\mathrm{example}:\:\:\mathrm{223}\:\mathrm{is}\:\mathrm{a}\:\mathrm{right}\:\mathrm{prime}\:\mathrm{because}\:\mathrm{despite}\:\mathrm{dropping}\:\mathrm{2}\:\mathrm{from}\:\mathrm{left} \\ $$$$\mathrm{most}\:\mathrm{part},\:\mathrm{we}\:\mathrm{obtain}\:\:\mathrm{23}\:\mathrm{as}\:\mathrm{the}\:\mathrm{prime}\:\mathrm{number}.\:\mathrm{Next},\:\mathrm{even}\:\mathrm{after}\:\mathrm{dropping}\: \\ $$$$\mathrm{2}\:\mathrm{from}\:\mathrm{left},\:\:\mathrm{3}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}. \\ $$$$\:\:\:\:\:\mathrm{How}\:\mathrm{many}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{right}\:\mathrm{prime}\:? \\ $$
Answered by MJS last updated on 20/Oct/18
we only have to check x3 and x7  13 17 23 37 43 47 53 67 73 83 97  11 numbers
$$\mathrm{we}\:\mathrm{only}\:\mathrm{have}\:\mathrm{to}\:\mathrm{check}\:{x}\mathrm{3}\:\mathrm{and}\:{x}\mathrm{7} \\ $$$$\mathrm{13}\:\mathrm{17}\:\mathrm{23}\:\mathrm{37}\:\mathrm{43}\:\mathrm{47}\:\mathrm{53}\:\mathrm{67}\:\mathrm{73}\:\mathrm{83}\:\mathrm{97} \\ $$$$\mathrm{11}\:\mathrm{numbers} \\ $$
Commented by Tawa1 last updated on 20/Oct/18
God bless you sir
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

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