On Thu, Aug 23, 2018 at 08:47:12AM -0700, Brent Meeker wrote: > > > On 8/22/2018 7:01 PM, Jason Resch wrote: > > There are also programs for which no one knows if they are computable or > > not. If you can prove whether or not this function ever completes, you > > will be world famous, and may even earn a million dollars (though I > > think the prize has been retracted, it might be oferred again): > > > > Step 1: Set X = 4 > > Step 2: Set R = 0 > > Step 3: For each Y from 1 to X, if both Y and (X – Y) are prime, set R = 1 > > Step 4: If R = 1, Set X = X + 2 and go to Step 2 > > Step 5: If R = 0, print X and halt > > > > All you have to prove is the computer either never gets to step 5 or > > that it does get to step 5. Mathematicians have been working on a > > related problem for 300 years, no one has solved it yet. > > X=6 so go to Step 2 and Set R=0 > When Y=2 and (X-Y)=4 they are not both prime. Leave R=0. > Go to step 5 print 6 and halt.
I read step 3 as a loop, ie check all Y from 1 to X (actually 1 to X/2 will suffice) before moving to step 4. In your example, the loop will check Y=3, and (X-Y)=3, so R=1, and so step 4 mean X=X+2 and step 2 is executed again. IIUC, if the twin primes conjecture were true, then the above program will never halt, but I could be wrong on that. Cheers -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow [email protected] Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
