A024351 Primes forming a 3 X 3 magic square with prime entries and minimal constant 177 = A164843(3).

5, 17, 29, 47, 59, 71, 89, 101, 113

Offset: 1

Author

Karl Schmerbauch (karl.j.schmerbauch(AT)boeing.com)

Keywords

• fini
• full
• nonn

Comments

The minimal 3 X 3 magic square made of consecutive primes has constant 4440084513 = A073520(3) = A270305(1), cf. A073519. - M. F. Hasler, Oct 22 2018

Sequence A073473 gives a variant using "primes including 1" (for historical reasons), to which also refers A073502. - M. F. Hasler, Oct 24 2018

Examples

			The square is [101 5 71 ; 29 59 89 ; 47 113 17].
The lexicographically smallest equivalent variant (modulo reflections on the symmetry axes of the square) is [17 89 71 ; 113 59 5 ; 47 29 101], cf. A320872. - _M. F. Hasler_, Oct 24 2018
		

Links

• Harvey Heinz, Prime Magic Squares
• Index entries for sequences related to magic squares

Crossrefs

Cf. A073350, A073520, A270305, A164843.

Cf. A073473, A073502.

Cf. A320872 (3 X 3 magic squares of primes), A268790 (magic sums of these).

Programs

PARI

A024351=select(p->setsearch(P,118-p),P=primes(30)[^5]) \\ 118 = 2*59, where 59 is the central prime; primes(30) = primes < 118. For the magic square itself, use A320872_row(1). -  M. F. Hasler, Oct 25 2018

Extensions

Offset corrected by Arkadiusz Wesolowski, Nov 26 2011