| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
This question came up while I was trying to solve this classical puzzle: A person thinks of 2 while numbers 2 through 99, and hands product to one mathematician, and sum to another. The two mathicians have the following conversation: Product: I don't know the 2 numbers Sum: I knew you didn't know Product: Now I know ! Sum: So do I ! Since sum knew product didn't know, sum isn't looking at a sum of 2 primes (because then sum would suppose product might be looking at product of those 2 primes and hence sum would have no way of knowing that product doesn't know the numbers). So, if sum isn't looking at a sum of 2 primes, does that mean he isn't looking at an even number (greater than 4) ? Actually, it is indeed the case for this particular puzzle, since all even numbers less than 200 are the sum of 2 primes. But it got me wondering in the general case: Is every even number the sum of 2 primes ? Can someone give a simple proof of this ? /Eric
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1880.1 | It's a famous problem | VMSDEV::HALLYB | Fish have no concept of fire | Wed Jun 29 1994 12:33 | 6 |
> Is every even number the sum of 2 primes ? Can someone give a simple
> proof of this ?
Goldbach beat you to this. Neither proof nor counterexample exists.
John
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| 1880.2 | a hint about original puzzle | HANNAH::OSMAN | see HANNAH::IGLOO$:[OSMAN]ERIC.VT240 | Wed Jun 29 1994 12:34 | 18 |
By the way, in case you want a hint about how to solve the original puzzle. Let's see if the 2 numbers could be 20 and 30. Product would be looking at 600. 600 primally is 2 * 2 * 2 * 3 * 5 * 5, so the 2 numbers could be 10,60 or 15,40 or 20,30 or 24,25. This means sum is looking at 70 or 45 or 50 or 49. We can immediately eliminate 45 or 49 since these are 2+43 and 2+47 which means sum would have no way of claiming "I know you didn't know". Actually, we can eliminate 70 and 45 also, since these are 3+67 and 3+47 so again sum would have no way of making the claim. So, actually it was pretty easy to show that 20 and 30 aren't the 2 numbers. /Eric | |||||