Interestingly (and unrelated to the comparison you made), if I change BigInteger and mpz_class to long, I still get the same answer but in 1.53 seconds for the C# and 1.61 seconds for C++. This suggests that aside from arbitrary precision math, C# may be as fast or faster than C++. What are your thoughts on this?

Another interesting point is that C++ still gets the right answers if I use double, while C# gives the wrong answer.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;
using System.Numerics;

namespace ConsoleApplication1
{
class Program
{
static void Main(string[] args)
{
Stopwatch start = Stopwatch.StartNew();

long b, a = 0;
double guess, root = Math.Sqrt(61.0);

BigInteger bi_a;
BigInteger bi_b;

while (a >= 0) // when a wraps around negateve, bail
{
a++;
guess = a * root;
b = (long)Math.Floor(guess);
bi_a = 61 * a * a + 1;
for (long j = 0; j < 1; j++) // change j < 1 to j < 2 if no answer found…
{
b += j;
bi_b = b * b;
if (bi_a == bi_b)
{
Console.Write("61 * " + a + "^2 + 1 = " + b + "^2\n");
Console.Write("\n\nFinished in Seconds: " + start.Elapsed.TotalSeconds + "\n");
Console.ReadKey();
}
}
}
}
}
}

Thanks for coming and leaving a comment. It is instructive for my main point, for you are involved in question begging where you tell me what I can’t prove. But that’s the point of discussion. That’s the topic. What is proof?

I am glad you spent a week proving that numbers exist. [Aside: Was this at BYU? You wouldn't happen to be a Mormon would you? Just curious, and that has nothing to do with anything.]

Your comments are doubly instructive, because you proved that numbers exist. That’s a very strange thing to do. I don’t prove that my phone exists, I just use it. I don’t prove that my chair exists, I just sit in it. Why would you prove that a number exists? Which makes me wonder, what do you think that it means for something to “exist”? Especially numbers? It is interesting that you appeal to your credentials and my lack of math courses. What you have done is made an appeal to facts that do have no bearing on your point. That my English is conversational or not, is neither here nor there (as my Numerical Analysis professor used to say).

I really am curious where you did your undergraduate work.

Sorry so late to reply, I was in Saudi Arabia when I saw your comment — just now back to the US having a chance to look over your request. Do you still need assistance? I can send you whatever you need. I can also send you y .EXE program that does what you speak of — but it sounds like you would like the source code to compile.

Steve

I’m trying to write a c# windows application that will allow me to post Tweets.

I noticed you had written a similar project, but the link on the site took me to a page saying project not uploaded yet.

All I really want to do for now is post tweets – can you help & advise me on how to do this please?

I working (free) on a campaign to raise public awareness of disability issues in the UK. Any help would be much appreciated.

Thanks
Tom