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FI-MO 2004 Problem 4

    The numbers 2005!+2,2005!+3,...,2005!+20052005! + 2, 2005! + 3, ... , 2005! + 2005 form a sequence of 20042004 consequtive integers, none of which is a prime number. Does there exist a sequence of 20042004 consequtive integers containing exactly 1212 prime numbers?

    Dataset text AI-MO AoPS. Quoted with source.

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