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Seqeunce with exactly 12 primes

Source: Finnish Mathematics Competition 2004, Final Round, Problem 4

November 14, 2011
number theoryprime numbersnumber theory unsolved

Problem Statement

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?
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