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.
Even in UBASIC, the computer can't do the factorial for numbers larger than 1014:
list
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
OK
run
4 5
6 103
10 329891
Illegal parameter in 20
?x
1015
OK
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 20100730 12:44:52 