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

%I #13 Oct 30 2018 20:15:24

%S 1,7,13,31,37,43,61,67,73

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

%C Until the early part of the twentieth century 1 was regarded as a prime (cf. A008578).

%C "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 "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 See A024351 for the "modern" version of the minimal 3 X 3 magic square of primes. - _M. F. Hasler_, Oct 30 2018

%D H. E. Dudeney, Amusements in Mathematics, Nelson, London, 1917, page 125.

%H Harvey Heinz, <a href="http://www.magic-squares.net/primesqr.htm">Prime Magic Squares</a>

%H <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>

%e The square is [ 43 1 67 / 61 37 13 / 7 73 31 ].

%Y Cf. A008578, A073350, A073502.

%Y Cf. A024351, A164843.

%K nonn,fini,full

%O 1,2

%A Lee Sallows (Sallows(AT)psych.kun.nl), Aug 27 2002