Problems & Puzzles: Puzzles

Puzzle 750. A special 5x5 prime magic square Here  we ask you to produce a 5x5 prime magic square such that: a) The concatenation of the primes in each row, from left to rigth, is a prime number. b) The concatenation of the primes in each column, from up to down, is a prime number. b) The concatenation of the primes in each diagonal, from up to down, is a prime number. Q. Send your solution with the minimal magic constant.

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Contributions came from Claudio Meller

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Claudio wrote:

One pandiagonal or 'diabolic' solution, with 8/12 primes:

1279       5009 1609       3929 31
1619       3931      7     1289    5011
17         1291 5021       1621    3907
5023      1597  3917        19        1301
3919         29 1303      4999     1607

Suma 11857

127950091609392931      Primo
16193931712895011       Primo
171291502116213907      Primo
502315973917191301
391929130349991607      Primo
127939315021191607      Primo
127916191750233919      Primo
500939311291159729
16097502139171303
392912891621194999      Primo
315011390713011607
311289502115973919      Primo

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Later on August 13 Claudio added:

Después de varios dìas encontré uno con 10

1973    2143    3923    631    587
3947    601    659    1913    2137
599    1907    2161    3917    673
2131    3989    613    593    1931
607    617    1901    2203    3929
 

Suma 9257

197321433923631587 VERDADERO
394760165919132137 FALSO
599190721613917673 VERDADERO
213139896135931931 VERDADERO
607617190122033929 VERDADERO
197360121615933929 VERDADERO
197339475992131607 VERDADERO
214360119073989617 VERDADERO
392365921616131901 VERDADERO
631191339175932203 VERDADERO
587213767319313929 VERDADERO
587191321613989607 FALSO
 

El menor que encontré de 8 con suma 827:


107    41    79    43    557
103    7    563    131    23
587    113    47    67    13
11    73    37    569    137
19    593    101    17    97

 

El menor que encontré de 9 con suma 1357

53    883    7    83    331
11    103    317    73    853
337    43    857    31    89
877    17    109    307    47
79    311    67    863    37

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Carlos Rivera and Claudio Meller wrote on August 18, 2014:

Using an algorithm provided by Claudio Meller and programmed and run in Ubasic by Carlos Rivera, they found another pandiagonal solution with 10/12 primes:
3 Rows: 1,2,4.
5 Colums: All.
2 Diagonals: Both

829 1003 1171 3 787
1061 269 523 1213 727
907 937 617 1327 5
883 1063 389 631 827
113 521 1093 619 1447

Magic sum = 3793

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