Prime Time

By

KT Rajagopalan

The question:

Prof Math EW is in a playful mood. He asks the students in his class to write their roll numbers on the blackboard. The forty of them do that: 316, 317, 318, … …, 355.

Now the professor asks one of them, Jaya, to erase any two of the roll numbers at random (say, a and b), and instead, write a new number (which should be the result of the operation ‘a + b – 1’).

Then he turns to Ramesh and says, ‘Ramesh, now there are thirty nine numbers on the blackboard. Erase any two of the numbers at random and do what Jaya did’.

This goes on till it was the turn of Esha, the fortieth student. The learned professor asks Esha, ‘You have no operation to perform. Just tell me one feature of this number.’

Esha thinks hard and says, ‘Sir, it is a prime number.’

What is the number left on the board at the end?

(a) 13381      (b) 13431      (c) 13411      (d) 13291      (e) 13121   

Would you like a hint?

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