OFFSET
1,1
COMMENTS
Each 3 X 3 magic square of consecutive primes can be described by three parameters: p1, b and c, where p1 is the smallest prime in the magic square, b > 0 and c > -b; the magic square is then given by:
+----------+----------+----------+
| p1+5b+2c | p1 | p1+4b+c |
+----------+----------+----------+
| p1+2b | p1+3b+c | p1+4b+2c |
+----------+----------+----------+
| p1+2b+c | p1+6b+2c | p1+b |
+----------+----------+----------+
If c > 0, the magic square is of type 1; if -b < c < 0, the magic square is of type 2. If the consecutive primes are given by p1, p2, ..., p9 (in increasing order), the magic square types are given by:
Type 1 Type 2
+----+----+----+ +----+----+----+
| p8 | p1 | p6 | | p8 | p1 | p7 |
+----+----+----+ +----+----+----+
| p3 | p5 | p7 | | p4 | p5 | p6 |
+----+----+----+ +----+----+----+
| p4 | p9 | p2 | | p3 | p9 | p2 |
+----+----+----+ +----+----+----+
LINKS
A.H.M. Smeets, Table of n, a(n) for n = 1..759
Harvey D. Heinz, Prime Numbers Magic Squares: Minimum consecutive primes - 3, 1999-2010.
A.H.M. Smeets, Python program
Eric Weisstein's World of Mathematics, Prime Magic Square
FORMULA
CROSSREFS
KEYWORD
sign,changed
AUTHOR
A.H.M. Smeets, Apr 07 2021
STATUS
approved