## Ultra Magic Squares of prime numbers

# Competition #3

This competition is organized by Макарова Наталия (Natalia Makarova)

## Definitions

### Definition 1:

Magic square is called ultra magic square, if it is both associative (center symmetric) and pandiagonal.

Ultra magic squares exist for orders n > 4.

## The Contest

In the contest is required to built ultra magic squares of order 7 – 16 of distinct primes.

Example

n = 5 113 1151 1229 911 101 839 521 41 1013 1091 941 953 701 449 461 311 389 1361 881 563 1301 491 173 251 1289 S=3505

This is the minimal solution for n = 5.

Known as a minimal solution for n = 6 (author M. Alekseyev)

103 59 163 233 139 293 229 257 307 131 13 53 283 17 67 173 181 269 61 149 157 263 313 47 277 317 199 23 73 101 37 191 97 167 271 227 S=990

### Rule:

For each order n = 7 – 16 you can imagine several solutions with magic constants S1 <S2 <S3 …

Known solutions:

n = 7, S = 4613 (author N. Makarova) n = 8, S = 2640 (author N. Makarova) n = 9, S = 24237 (author A. Chernov)

Contestant shall not be deemed a winner, if he would submit only solutions with known magic constants

## Format of solution

The solution is represented in the form:

n: a (1), a (2), a (3), …, a (n^2)

Example:

5:113,1151,1229,911,101,839,521,41,1013,1091,941,953,701,449,461,311,389,1361,881,563,1301,491,173,251,1289

## Scoring

Contestant receives for every *n* the score: *Smin/S*, where

*Smin* – the minimal magic constant of solution in the contest;

*S* – the minimal magic constant of solution by contestant.

## The Prize

Winner receives a prize of 3000 rubles.

If the winner is not from Russia, the prize will be paid in $USA at the official rate on the day of end the contest.

Organizers *N. Makarova* and *S. Tognon* can participate in the contest, but does not receive the prize in case of winning.