A073473 -id:A073473 - cp's OEIS frontend

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

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

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

			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

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

Cf. A073350, A073520, A270305, A164843.
Cf. A073473, A073502.
Cf. A320872 (3 X 3 magic squares of primes), A268790 (magic sums of these).

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

Offset corrected by Arkadiusz Wesolowski, Nov 26 2011

A073502 The smallest magic constant for n X n magic square with prime entries (regarding 1 as a prime).

Original entry on oeis.org

111, 102, 213, 408, 699, 1114, 1681, 2416, 3355, 4514, 5937, 7626, 9635, 11986, 14691, 17818, 21373, 25394, 29873, 34926, 40511, 46664, 53445, 60898, 69045, 77888, 87473, 97850, 109065, 121126, 134113, 147982, 162759

Offset: 3

N. J. A. Sloane, Aug 27 2002

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

W. S. Andrews and H. A. Sayles, The Monist (Chicago) for October 1913.
H. E. Dudeney, Amusements in Mathematics, Nelson, London, 1917, page 125, who quotes the Andrews-Sayles article as his source.

Yu. V. Chebrakov, Section 3.3. Smallest magic matrices of prime numbers in "Theory of Magic Matrices. Issue TMM-1.", 2008. (in Russian)
N. Makarova 13 X 13 magic square. (in Russian)
N. Makarova 14 X 14 magic square. (in Russian)
Eric Weisstein's World of Mathematics, Prime Magic Square
Index entries for sequences related to magic squares

Cf. A073473 (for the n=3 square), A024351, A073520, A164843, A173079.

Dudeney gives 36095/11 for n = 11 (an obvious typo) and 4514 for n = 12
a(3)-a(12) are confirmed/given by Chebrakov
a(15), a(17), a(22), a(35), and a(124)=9912840 from S. Tognon (cf. A173079)
a(13)-a(14), a(16), a(18)-a(21), a(23)-a(34) from N. Makarova
Edited by Max Alekseyev, Feb 11 2010

A073350 Primes not at the center of a 3 X 3 magic square of primes.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 79, 83, 97, 101, 107, 113, 163, 181, 197, 199, 223, 229, 233, 277, 313, 317, 331, 433, 439, 457, 569, 859

Offset: 1

David W. Wilson, Aug 25 2002

nonn

The "magic sum" is always thrice the central entry.
There are no other terms < 5000.
There are no other terms < 100000. - Robert Israel, Feb 16 2016

Index entries for sequences related to magic squares

Cf. A073473. A magic square with 59 at center is given in A024351.

N:= 10000: # to get all terms <= N
P:= select(isprime,{seq(p,p=3..2*N,2)}):
count:= 1:
A[count]:= 2:
for ic from 1 while P[ic] <= N do
   c:= P[ic];
   V:= map(`-`,P[ic+1..-1],c) intersect map(t -> c-t, P[1..ic-1]);
   nv:= nops(V);
   VV:= {seq(seq(V[j]-V[i],j=i+1..nv),i=1..nv-1)} intersect V;
   nvv:= nops(VV);
   found:= false;
   for ia from 1 to nvv while not found do
     a:= VV[ia];
     for ib from ia+1 to nvv while VV[ib] < c - a do
       b:= VV[ib];
       if b <> 2*a and {c-a-b,c-a+b,c-b+a,c+a+b} subset P then
          found:= true;
          break
       fi
     od
   od:
   if not found then
     count:= count+1;
     A[count]:= c;
   fi
od:
seq(A[i],i=1..count); # Robert Israel, Feb 16 2016

cp's OEIS Frontend

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

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A073502 The smallest magic constant for n X n magic square with prime entries (regarding 1 as a prime).

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A073350 Primes not at the center of a 3 X 3 magic square of primes.

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