Evil Mark stood up in the middle of the afternoon and said "I'm about to hand out sheets listing the 8,363 prime numbers between 10,000 and 100,000. Embedded in this list is one non-prime. First person to find that non-prime number wins my Family Guy promotional sixteen-ounce beer cozy."The next several pages contained lots of large numbers. The reference to Goldbach's Conjecture might suggest that there is an even number somewhere in the list, but that would seem a comedown from the guy who once encoded a passage in binary.
In less than five minutes I won.
FUN FACT: any even number can be made by adding together two primes.
Any ideas?
5 comments:
Do we get to see the list of numbers, or what?
I don't have the numbers. Here's a list of primes which should contain all those in the book, less the non-prime. If the impostor wasn't even, then perhaps there's a fast strategy to identify any odd composite inserted into the list.
Primes ( > 2) must end in 1, 3, 7, or 9. Other than that, I don't know a fast way.
BTW, the fun fact is false (it's not an accurate statement of Goldbach).
If anybody wants to do some checking, I scanned the book up to around 31469 looking for non-prime end digits, taking six minutes.
Other than omitting the >2 clause and not making it clear that it hasn't been proved, why isn't the fun fact a fair expression of Goldbach's Conjecture?
Someone has lately updated the article and pointed out that it was Euler who expressed the familiar ("strong") version of the conjecture, and considered it "ein ganz gewisses Theorema."
After my last comment, I printed out that list of primes with the same number of columns and lines and compared it to the book. I checked the first and last number on each page and a few random numbers here and there and everything matched. So, contrary to what the instructions imply, if there is a composite in the list it seems to have taken the place of a prime.
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