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Goldbach Conjecture: Closer To Solved?
mikejuk writes "The Goldbach conjecture is not the sort of thing that relates to practical applications, but they used to say the same thing about electricity. The Goldbach conjecture is reasonably well known: every integer can be expressed as the sum of two primes. Very easy to state, but it seems very difficult to prove. Terence Tao, a Fields medalist, has published a paper that proves that every odd number greater than 1 is the sum of at most five primes. This may not sound like much of an advance, but notice that there is no stipulation for the integer to be greater than some bound. This is a complete proof of a slightly lesser conjecture, and might point the way to getting the number of primes needed down from at most five to at most 2. Notice that no computers were involved in the proof — this is classical mathematical proof involving logical deductions rather than exhaustive search."
I hereby prove that every even number is a sum of no more than six primes, one of those is 1.
Wow, what has slashdot come to when posts are getting modded up for posting basic arithmetic :)
7 + 2 = 9
Damn, that's the most intelligent post I've seen on Slashdot all day, and I mis-clicked and chose 'redundant' when moderating...
7 + 2 + 2
Ah, Mexican Math, we meet again. That's not two primes. That's three primes, two of which are 2.
Notice that no computers where involved in the proof — this is classical mathematical proof involving logical deductions rather than exhaustive search.
Exhaustive search for a result that holds for every integer? Good luck with that one.
Everyone knows integers only go from 0 to 4294967295!
That will treat me to reed my messages before posting.
Alas, it did not treat you.
They recently discovered a few more: 4294967296 through 18446744073709551615. Just in time too--we were starting to run out in some computations. Unfortunately it'll take a bit longer to verify the conjecture for these newly discovered specimens. At least there's only a finite number of primes...
Not so, 8561290356012956901265912656135612056135460123560912356102650931951 and 653 are prime. They sum to your number.
a,e,i,o,u and sometimes w and y (at be if of up cwm by)
You youngsters... I remember telling that joke with 32768.
Unicode killed the ASCII-art *
I'm going to eat 5 donuts a day while masturbating to pictures of Angela Merkel. It's not the sort of thing that relates to practical applications, but they used to say the same thing about electricity.