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A073473 Primes (including 1) forming 3 X 3 magic square with prime entries and minimal constant 111 = A073502(3).

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%I A073473 #13 Oct 30 2018 20:15:24
%S A073473 1,7,13,31,37,43,61,67,73
%N A073473 Primes (including 1) forming 3 X 3 magic square with prime entries and minimal constant 111 = A073502(3).
%C A073473 Until the early part of the twentieth century 1 was regarded as a prime (cf. A008578).
%C A073473 "The problem of constructing magic squares with prime numbers only was first discussed by myself in The Weekly Dispatch for Jul 22 1900 and Aug 05 1900; but during the last three or four years it has received great attention from American mathematicians. First, they have sought to form these squares with the smallest possible constants.
%C A073473 "Thus the first nine prime numbers, 1 to 23 inclusive, sum to 99, which (being divisible by 3) is theoretically a suitable series; yet it has been demonstrated that the smallest possible constant is 111 and the required series as follows: 1,7,13,31,37,43,61,67,73." - Dudeney
%C A073473 See A024351 for the "modern" version of the minimal 3 X 3 magic square of primes. - _M. F. Hasler_, Oct 30 2018
%D A073473 H. E. Dudeney, Amusements in Mathematics, Nelson, London, 1917, page 125.
%H A073473 Harvey Heinz, <a href="http://www.magic-squares.net/primesqr.htm">Prime Magic Squares</a>
%H A073473 <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>
%e A073473 The square is [ 43 1 67 / 61 37 13 / 7 73 31 ].
%Y A073473 Cf. A008578, A073350, A073502.
%Y A073473 Cf. A024351, A164843.
%K A073473 nonn,fini,full
%O A073473 1,2
%A A073473 Lee Sallows (Sallows(AT)psych.kun.nl), Aug 27 2002