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The set of nine consecutive primes forming a 3 X 3 magic square with the smallest magic constant (4440084513).
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%I #31 Oct 28 2018 09:11:46

%S 1480028129,1480028141,1480028153,1480028159,1480028171,1480028183,

%T 1480028189,1480028201,1480028213

%N The set of nine consecutive primes forming a 3 X 3 magic square with the smallest magic constant (4440084513).

%C The square is given (with the terms in correct order) in A320873. The (increasingly ordered) set of primes does not contain more information than the magic constant (= sum) S, since they have to be consecutive and sum up to 3*S. It is easy to construct the unique set of (consecutive) primes with this property, cf. PROGRAM. - _M. F. Hasler_, Oct 28 2018

%D H. L. Nelson, Journal of Recreational Mathematics, 1988, vol. 20:3, p. 214.

%D Clifford A. Pickover, The Zen of Magic Squares, Circles and Stars: An Exhibition of Surprising Structures across Dimensions, Princeton University Press, 2002.

%H Harvey D. Heinz, <a href="http://www.magic-squares.net/primesqr.htm#Minimum consecutive primes -3">Prime Numbers Magic Squares: Minimum consecutive primes - 3</a>, 1999-2010.

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

%e The magic square is

%e [ 1480028201 1480028129 1480028183 ]

%e [ 1480028153 1480028171 1480028189 ]

%e [ 1480028159 1480028213 1480028141 ]

%o (PARI) A073519=MagicPrimes(4440084513,3) \\ where: (also used in A073521, ...)

%o MagicPrimes(S, n, P=[nextprime(S\n)])={S=n*S-P[1]; for(i=1, -1+n*=n, S-=if(S>(n-i)*P[1], P=concat(P, nextprime(P[#P]+1)); P[#P], P=concat(precprime(P[1]-1), P); P[1])); if(S, -P, P)} \\ The vector of n^2 primes whose sum is n*S, or a negative vector with an approximate solution if no exact solution exists. - _M. F. Hasler_, Oct 22 2018

%Y Cf. A024351, A073520, A073521, A073522, A073523, A256891, A265139, A265614.

%K nonn,fini,full

%O 1,1

%A _N. J. A. Sloane_, Aug 29 2002