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molt_llest
- Senior | Next Rank: 100 Posts
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- Joined: Sat May 10, 2008 3:05 pm
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First, the question really asks: "Is k prime?"
From 1)- knowing k is larger than 4! is not enough. There is an infinite number of primes; this kind of statement cannot possibly help.
From 2)- k is between 13!+2 and 13!+13. None of the numbers in this list can be prime. I'll take one example, 13! + 11. Notice that 13! is a multiple of 11 (it's 13*12*11*...). When you add two multiples of 11, you get another multiple of 11. 13!+11 is a multiple of 11, and is not prime. This statement is sufficient.
In full detail:
13! + 11 = 11*(13*12*10! + 1)
13! + 11 is thus a multiple of 11 and also a multiple of 13*12*10! + 1, and is not prime.
