CF80A Panoramix's Prediction
Description
A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers $ 2 $ , $ 7 $ , $ 3 $ are prime, and $ 1 $ , $ 6 $ , $ 4 $ are not.
The next prime number after $ x $ is the smallest prime number greater than $ x $ . For example, the next prime number after $ 2 $ is $ 3 $ , and the next prime number after $ 3 $ is $ 5 $ . Note that there is exactly one next prime number after each number. So $ 5 $ is not the next prime number for $ 2 $ .
One cold April morning Panoramix predicted that soon Kakofonix will break free from his straitjacket, and this will be a black day for the residents of the Gallic countryside.
Panoramix's prophecy tells that if some day Asterix and Obelix beat exactly $ x $ Roman soldiers, where $ x $ is a prime number, and next day they beat exactly $ y $ Roman soldiers, where $ y $ is the next prime number after $ x $ , then it's time to wait for Armageddon, for nothing can shut Kakofonix up while he sings his infernal song.
Yesterday the Gauls beat $ n $ Roman soldiers and it turned out that the number $ n $ was prime! Today their victims were a troop of $ m $ Romans ( $ m>n $ ). Determine whether the Gauls should wait for the black day after today's victory of Asterix and Obelix?
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