If 11x+5y is a prime number where x, y are natural numbers then what is the <strong>MINIMUM</strong> value of (x+y)?

Explanation

We test small natural numbers (x, y \geq 1) to minimize (x+y). For x+y=2 \implies (1,1), 11(1)+5(1)=16 (not prime). For x+y=3, combinations (1,2) and (2,1) yield 21 and 27 (not prime). For x+y=4, combinations yield 26, 32, 38 (not prime). For x+y=5, using (1,4) yields 11(1)+5(4)=31, which is a prime number. Minimum value is 5.

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