All prime numbers

Number Theory Level 3

In the first column we have the numbers from 1 to N (where N is odd). We want to put in the second column the same numbers from 1 to N, in the order that is convenient, so that all sums result in a prime number. After which number in the first column will we have to put the 1?


The answer is 1.

Ronald Chén by Ronald Chén , 32, Guatemala

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Ronald Chén
Dec 23, 2016

The 1 has to go with the 1. Explanation: Being odd N, between the numbers from 1 to N, odd numbers are one more than pairs. And so, when couples are made, we can not prevent two odd pairing. And that only gives cousin with 1 + 1 = 2.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

This is interesting. If there is arrangement that works then 1 1 will necessarily be paired with 1 1 . I'm not sure, though, if it is a given that there will be an arrangement that works for every odd N N . I've quickly checked up to N = 33 N = 33 without any problems and I'm sure I could keep going higher, but I'm not sure I could keep going higher indefinitely. When the prime gaps start to get larger I would anticipate some difficulties. I'll have to see if I can come up with either a proof or a counterexample.

Brian Charlesworth - 4 years, 5 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...