(In reply to re(4): For those who wanna try
UBASIC is available at http://archives.math.utk.edu/software/msdos/number.theory/ubasic/.html
A link to download QuickBasic 4.5 is available at http://www.qbcafe.net/english/
I don't know if these are the "sophisticated tools" to which you refer, but they are DOS programs and thus a bit old.
I do avoid posting in a time less than it takes me to solve the puzzle, and in fact wait somewhat more, but this puzzle's computer solution was very straightforward. The nxtprm function of UBASIC allowed solution via a rather easy program, taking 3 primes at a time and advancing the group of three.
I would certainly be interested in seeing what logic can lead to the solution without the program, and I can't imagine why a computer solution would take the place of (or,in other words, prevent) an analytic solution, as I'm sure many would welcome that.
Posted by Charlie
on 2006-01-17 09:10:08