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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.

%I A364538 #16 Aug 02 2023 15:48:13
%S A364538 1,823,821,809,811,797,19,29,313,31,23,37,89,83,211,79,641,631,619,
%T A364538 709,617,53,43,739,97,227,103,107,193,557,719,727,607,139,757,281,223,
%U A364538 653,499,197,109,113,563,479,173,761,587,157,367,379,521,383,241,467,257,263,269,167,601,599
%N 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.
%C A364538 This magic square was discovered in 1913 by J. N. Muncey.
%C A364538 12 is the smallest order possible for a nontrival magic square of this type. The magic sum is 4514.
%D A364538 Martin Gardner, The Sixth Book of Mathematical Games from Scientific American, Chicago, IL, University of Chicago Press, 1984, pp. 86-87.
%H A364538 Paolo Xausa, <a href="/A364538/b364538.txt">Table of n, a(n) for n = 1..144</a> (rows 1..12 of the square, flattened)
%H A364538 W. S. Andrews and H. A. Sayles, <a href="https://www.jstor.org/stable/27900468">Magic squares made with prime numbers to have the lowest possible summations</a>, The Monist, Vol. 23, No. 4, 1913, pp. 623-630.
%H A364538 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeMagicSquare.html">Prime Magic Square</a>.
%H A364538 <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>
%e A364538 The magic square is:
%e A364538   [   1 823 821 809 811 797  19  29 313  31  23  37 ]
%e A364538   [  89  83 211  79 641 631 619 709 617  53  43 739 ]
%e A364538   [  97 227 103 107 193 557 719 727 607 139 757 281 ]
%e A364538   [ 223 653 499 197 109 113 563 479 173 761 587 157 ]
%e A364538   [ 367 379 521 383 241 467 257 263 269 167 601 599 ]
%e A364538   [ 349 359 353 647 389 331 317 311 409 307 293 449 ]
%e A364538   [ 503 523 233 337 547 397 421  17 401 271 431 433 ]
%e A364538   [ 229 491 373 487 461 251 443 463 137 439 457 283 ]
%e A364538   [ 509 199  73 541 347 191 181 569 577 571 163 593 ]
%e A364538   [ 661 101 643 239 691 701 127 131 179 613 277 151 ]
%e A364538   [ 659 673 677 683  71  67  61  47  59 743 733  41 ]
%e A364538   [ 827   3   7   5  13  11 787 769 773 419 149 751 ]
%Y A364538 Cf. A073502, A173079.
%K A364538 nonn,tabf,fini,full
%O A364538 1,2
%A A364538 _Paolo Xausa_, Jul 28 2023