A364538 A 12 X 12 magic square composed of 1 and the first consecutive odd primes with the smallest possible magic sum, read by rows.

1, 823, 821, 809, 811, 797, 19, 29, 313, 31, 23, 37, 89, 83, 211, 79, 641, 631, 619, 709, 617, 53, 43, 739, 97, 227, 103, 107, 193, 557, 719, 727, 607, 139, 757, 281, 223, 653, 499, 197, 109, 113, 563, 479, 173, 761, 587, 157, 367, 379, 521, 383, 241, 467, 257, 263, 269, 167, 601, 599

Offset: 1

Author

Paolo Xausa, Jul 28 2023

Keywords

• nonn
• tabf
• fini
• full

Comments

This magic square was discovered in 1913 by J. N. Muncey.

12 is the smallest order possible for a nontrival magic square of this type. The magic sum is 4514.

Examples

			The magic square is:
  [   1 823 821 809 811 797  19  29 313  31  23  37 ]
  [  89  83 211  79 641 631 619 709 617  53  43 739 ]
  [  97 227 103 107 193 557 719 727 607 139 757 281 ]
  [ 223 653 499 197 109 113 563 479 173 761 587 157 ]
  [ 367 379 521 383 241 467 257 263 269 167 601 599 ]
  [ 349 359 353 647 389 331 317 311 409 307 293 449 ]
  [ 503 523 233 337 547 397 421  17 401 271 431 433 ]
  [ 229 491 373 487 461 251 443 463 137 439 457 283 ]
  [ 509 199  73 541 347 191 181 569 577 571 163 593 ]
  [ 661 101 643 239 691 701 127 131 179 613 277 151 ]
  [ 659 673 677 683  71  67  61  47  59 743 733  41 ]
  [ 827   3   7   5  13  11 787 769 773 419 149 751 ]
		

References

• Martin Gardner, The Sixth Book of Mathematical Games from Scientific American, Chicago, IL, University of Chicago Press, 1984, pp. 86-87.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..144 (rows 1..12 of the square, flattened)
• W. S. Andrews and H. A. Sayles, Magic squares made with prime numbers to have the lowest possible summations, The Monist, Vol. 23, No. 4, 1913, pp. 623-630.
• Eric Weisstein's World of Mathematics, Prime Magic Square.
• Index entries for sequences related to magic squares

Crossrefs

Cf. A073502, A173079.