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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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re: computer can't go that high | Comment 2 of 9 |
(In reply to computer can't go that high by Charlie)

Charlie,

x = 28 is another solution found here, and is the only other valid value under 400.

I came across this Java-based factorization program to help extend the search up to x = 5983, just to find the values that AREN'T prime, since we only need the probable prime test to fail to show that a value is composite.

There's no way we ourselves can check all of the values within the range requested, as the values are just too large to work with. Perhaps x = 4, 6, 10, and 28 are the only possible values and the probability is a nice round 1 / 5000 or 0.02%?
  Posted by Justin on 2010-07-30 17:55:26

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