Nice @Don! That's something I was thinking but couldn't come up with the name.
Finding a large prime itself is already an interesting and difficult thing in number theory. To prove something on top of that could be even more difficult On Mar 24, 12:38 pm, Don <[email protected]> wrote: > This is called Goldbach's Conjecture, and has not yet been proven or > disproven. > > Goldbach wrote a letter to Euler in 1742 suggesting that every integer > n > 5 is the sum of three primes. Euler replied that this is > equivalent to every even n > 2 is the sum of two primes--this is now > known as Goldbach's conjecture. Schnizel showed that Goldbach's > conjecture is equivalent to every integer n > 17 is the sum of three > distinct primes. > > It has been proven that every even integer is the sum of at most six > primes and in 1966 Chen proved every sufficiently large even integer > is the sum of a prime plus a number with no more than two prime > factors (a P2). In 1993 Sinisalo verified Goldbach's conjecture for > all integers less than 4*10^11. More recently Jean-Marc Deshouillers, > Yannick Saouter and Herman te Riele have verified this up to 10^14 > with the help, of a Cray C90 and various workstations. In July 1998, > Joerg Richstein completed a verification to 4*10^14 and placed a list > of champions online. More recent work by Oliveira e Silva has extended > this to at least 4*10^17. > > There has been substantial progress on proving that every odd integer> 5 is > the sum of 3 primes, the easier case of Goldbach's conjecture. > > In 1937 Vinogradov proved that this is true for sufficiently large odd > integers n. In 1956 Borodzkin showed n > 3^14348907 is sufficient > (the exponent is 3^15). In 1989 Chen and Wang reduced this bound to > 10^43000. The exponent still must be reduced dramatically before we > can use computers to take care of all the small cases. > > Don > > On Mar 24, 12:49 am, bittu <[email protected]> wrote: > > > > > > > > > yesterday one of the my friends asked this Q to me prove with > > correctness that > > "Every even integer greater than 2 can be expressed as the sum of two > > primes" > > e.g > > > 4 = 2 + 2 > > 6 = 3 + 3 > > 10 = 7 + 3 or 5 + 5 > > 14 = 3 + 11 or 7 + 7 > > > Explain & Derive The Time ,Space Complexity of Algorithm > > > it seems to be that we have to find all possible prime factor of > > number & prints it its not big task , so by checking that number we > > have to generate the all prime factor of it seems O(n) ..Hope i m > > clear corrcet me if i am wrong here.?? > > > But problem come when even number become bigger say 1 billion 10^9 > > so for this choosing the a number as a prime factor has probability of > > 1/ln(n) > > so say if for 1 billion number out of 21 only 1 is prime. .y question > > is we have to prove the time complexity for two > > choosing a number nearby such big number is 1/ln(n)..?? > > > with Heuristic justification it can be explained ro induction might > > help but guarantee here but i need some > > mathematical proof for this > > > Thank & Regards > > Shashank Mani > > CSE,BIT Mesra -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
