Le Monde puzzle [#6]

A simple challenge in Le Monde this week: find the group of four primes such that any sum of three terms in the group is prime and the overall sum is minimised. Here is a quick exploration by simulation, using the schoolmath package (with its imperfections):


for (t in 1:10^4){

 for (j in 2:4)

 if ((sto)&(sum(B)<res)){

providing the solution 5 7 17 19.

A subsidiary question in the same puzzle is whether or not it is possible to find a group of five primes such that any sum of three terms is still prime. Running the above program with the proper substitutions of 4 by 5 does not produce any solution, even when increasing the upper boundary in A. So it is most likely that the answer is no.

One Response to “Le Monde puzzle [#6]”

  1. The solution to the five prime problem appeared yesterday in Le Monde: consider five primes


    satisfying the constraints. Then necessarily at most two of them takes the same value modulo 3. This implies that there exist

    a_{i_1}\equiv 0\mod 3, a_{i_2}\equiv 1\mod 3, a_{i_3}\equiv 2\mod 3.


    a_{i_1}+a_{i_1}+a_{i_2}\equiv 0\mod 3

    cannot be a prime number.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


Get every new post delivered to your Inbox.

Join 919 other followers