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A073519 The set of nine consecutive primes forming a 3 X 3 magic square with the smallest magic constant (4440084513). 20
1480028129, 1480028141, 1480028153, 1480028159, 1480028171, 1480028183, 1480028189, 1480028201, 1480028213 (list; graph; refs; listen; history; text; internal format)



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


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

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


Table of n, a(n) for n=1..9.

Harvey D. Heinz, Prime Numbers Magic Squares: Minimum consecutive primes - 3, 1999-2010.

Index entries for sequences related to magic squares


The magic square is

[ 1480028201 1480028129 1480028183 ]

[ 1480028153 1480028171 1480028189 ]

[ 1480028159 1480028213 1480028141 ]


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

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


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

Sequence in context: A129249 A165736 A048051 * A256891 A320873 A166113

Adjacent sequences:  A073516 A073517 A073518 * A073520 A073521 A073522




N. J. A. Sloane, Aug 29 2002



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Last modified January 19 16:32 EST 2019. Contains 319309 sequences. (Running on oeis4.)