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The "How many primes between N! + 2 and N! + 7" qu

Problem Solving — algebra and arithmetic
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by tennisdiva » Wed Apr 07, 2010 4:03 am
So I often see this type of question appear: how many primes are there between 9! + 2 and 9! + 8. The answer is none because 9! = 9*8*7.... *2*1, since 9! is a multiple of 2, adding 2 means it's still a multiple of 2 and hence not prime. However, if the question were to ask, 9! + 12, this is also 9! + 5 + 7, so does this mean this is also not prime? So to generalize, can we say there are no primes between 9! + 1 to 9! + (9+8+7.....+ 2+1)?
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by GMATdawg » Wed Apr 07, 2010 9:02 am
You are correct - they're are no prime numbers between 9! + 1 and 9! + 9.. or 362,881 and 362,889.

I used this site to double check - https://www.apples4theteacher.com/prime-factors.html
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