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(x!+1)/(x+1) = prime number (Posted on 2010-07-30) Difficulty: 3 of 5
For a positive integer x drawn at random between 1 and 20000 inclusively, determine the probability that (x!+1)/(x+1) is a prime number.

No Solution Yet Submitted by K Sengupta    
Rating: 2.3333 (3 votes)

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Wilson Quotient Values | Comment 4 of 9 |
What I have noticed, when putting the numbers into an excelspreadsheet is that the first few primes
5, 103, 329891, 36846277 and 1230752346353 are Wilson Quotient values.   They seem to be coming up with prime numbers when you let x = a prime - 1.  

I don't know how to prove this but my guess is that the number would be the amount of primes less than 2000 (subtracting the #2 and #3 because those both give values of 1 from the equation).  

  Posted by Paul on 2010-07-30 18:55:34
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