View previous topic | View next topic


Page 1 of 1

11773.  Thu Dec 02, 2004 7:50 pm Reply with quote

Goldbach's Conjecture is that every even number is the sum of two prime numbers - eg 6=3+3, 12=7+5, 30=17+13. This has been verified as true in practice for numbers up to a very great magnitude, but no-one has ever found a theoretical proof.
One can verify Goldbach's conjecture by brute force, up to a point. By using about 130 CPU-hours on an IBM 3083 Sinisalo (1993) verified the conjecture up to 4*10^11. Although Sinisalo used a bit array and Eratosthenes sieve, the QBASIC program that follows the similar strategy while employing trial division. The procedure is to take an odd number and then find small primes starting with 3, up to n/2. If p is prime then the difference n - p is tested for primality. If the difference is prime then we are done we have found a pair.

Any other curious conjectures we should know about?

11774.  Thu Dec 02, 2004 8:04 pm Reply with quote

I don't know about anyone else, but I found that HIGHLY counter-intuitive.

11779.  Fri Dec 03, 2004 5:24 am Reply with quote

There's Karl Popper's seminal 1963 book Conjectures and Refutations, which lays out the fundamental philosophy for the growth of scientific knowledge. It says that a conjecture comes first, it is then tested empirically, and if it can't be refuted by experiment, it survives to 'fight another day'.

In this way, scientific knowledge grows in a evolutionary cycle of adaptation to the world. Just like biological life. You end up with something breathtakingly complex, beautiful and powerful, and mankind only acted as a sort of joint midwife and grave-digger.

One of the most important books in modern science.


Page 1 of 1

All times are GMT - 5 Hours

Display posts from previous:   

Search Search Forums

Powered by phpBB © 2001, 2002 phpBB Group