A073519 The set of nine consecutive primes forming a 3 X 3 magic square with the smallest magic constant (4440084513).

1480028129, 1480028141, 1480028153, 1480028159, 1480028171, 1480028183, 1480028189, 1480028201, 1480028213

Offset: 1

Author

N. J. A. Sloane, Aug 29 2002

Keywords

• nonn
• fini
• full

Comments

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

Examples

			The magic square is
[ 1480028201 1480028129 1480028183 ]
[ 1480028153 1480028171 1480028189 ]
[ 1480028159 1480028213 1480028141 ]
		

References

• 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.

Links

• Harvey D. Heinz, Prime Numbers Magic Squares: Minimum consecutive primes - 3, 1999-2010.
• Index entries for sequences related to magic squares

Crossrefs

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

Programs

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