A073473 Primes (including 1) forming 3 X 3 magic square with prime entries and minimal constant 111 = A073502(3).

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

Offset: 1

Author

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

Keywords

• nonn
• fini
• full

Comments

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

"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.

"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

See A024351 for the "modern" version of the minimal 3 X 3 magic square of primes. - M. F. Hasler, Oct 30 2018

Examples

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

References

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

Links

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

Crossrefs

Cf. A008578, A073350, A073502.

Cf. A024351, A164843.