Problems & Puzzles: Puzzles

Puzzle 1016. Vector of primes such that... Carlos Rivera propose the following puzzle: Find the vector of K ordered distinct primes of increasing value, with the minimal sum of these primes, such that concatenated produce a prime, and the same after circular rolling of all the primes in the vector.   Examples:   K Vector Sum 2 3, 7 10 3 7, 13, 17 37 4 13, 19, 23, 37 92 5 3, 7, 13, 37, 43 103 6 3, 7, 43, 53, 59, 97 262 7 19, 31, 43, 47, 53, 67, 113 373 8 7, 37, 47, 59, 97, 103, 137, 151 638 Example. K=3, Vector={ 7, 13, 17}, 7.13.17, 13.17.7 and17.7.13 are primes and 37 is minimal sum of the primes in the Vector. Q1. Extend the Table for K=9 to ...

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On week 4-11 Set. 2020, contributions came from Paul Cleary, Giorgos Kalogeropoulos, Emmanuel Vantieghem

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Paul wrote:

I don’t have a new addition to this problem yet, but as a check that my program is working I check it against your published solutions and I do believe that there is a smaller sum total for K=6 with these primes:-

 214 , {3,13,19,23,29,127}

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Giorgos wrote:

Here is my answer for K=9
 

K=9

Vector={3,11,17,23,29,41,47,61,211}

Sum=443

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Emmanuel wrote:

For  K = 6  I found the vector  {3,13,19,23,29,127}  with a total of 214.

The other examples are indeed minimal.

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