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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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Some Thoughts computer can't go that high | Comment 1 of 9

Even in UBASIC, the computer can't do the factorial for numbers larger than 1014: 

   10   for X=3 to 20000
   20   if (!(X)+1)@(X+1)=0 then
   30   :Q=(!(X)+1)//(X+1)
   40   :if prmdiv(Q)=Q then print X;Q
  100   next
 4  5
 6  103
 10  329891
Illegal parameter in 20

but we do see that even below that number, the only three valid X values (4, 6 and 10) are at the beginning of the range, but we don't know if the valid numbers just thin out rapidly or whether these three values are the only values.

  Posted by Charlie on 2010-07-30 12:44:52
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