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Flash

11773. Thu Dec 02, 2004 7:50 pm 


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 noone has ever found a theoretical proof.
Quote:  One can verify Goldbach's conjecture by brute force, up to a point. By using about 130 CPUhours 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. 
http://www.petrospectechnologies.com/Herkommer/goldbach.htm
Any other curious conjectures we should know about? 




Flash

11774. Thu Dec 02, 2004 8:04 pm 


I don't know about anyone else, but I found that HIGHLY counterintuitive. 




Gray

11779. Fri Dec 03, 2004 5:24 am 


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 gravedigger.
One of the most important books in modern science. 




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