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Question

If the product of two twin prime numbers and the absolute difference of smallest composite number and the smallest prime number is 646, then larger prime number is

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Solution

Smallest composite number is 4
Smallest prime number is 2
So, x(x+2)(42)=646
x(x+2)=323
x2+2x323=0
x2+19x17x323=0
(x+19)(x17)=0
Since, x=19 (not possible)
x=17

Hence, larger prime number is x+2=19




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