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A073473 Primes (including 1) forming 3 X 3 magic square with prime entries and minimal constant 111 = A073502(3). 3
1, 7, 13, 31, 37, 43, 61, 67, 73 (list; graph; refs; listen; history; text; internal format)



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


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


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

Harvey Heinz, Prime Magic Squares

Index entries for sequences related to magic squares


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


Cf. A008578, A073350, A073502.

Cf. A024351, A164843.

Sequence in context: A063583 A065764 A273757 * A272407 A040084 A151723

Adjacent sequences:  A073470 A073471 A073472 * A073474 A073475 A073476




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



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Last modified January 20 17:05 EST 2019. Contains 319335 sequences. (Running on oeis4.)