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Consecutive Primes

Source: ToT - 2001 Fall Senior O-Level #2

August 17, 2011
number theoryprime numbersnumber theory unsolved

Problem Statement

There exists a block of 1000 consecutive positive integers containing no prime numbers, namely, 1001!+2,1001!+3,...,1001!+10011001!+2,1001!+3,...,1001!+1001. Does there exist a block of 1000 consecutive positive intgers containing exactly five prime numbers?
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