{"id":19258,"date":"2026-06-08T03:41:41","date_gmt":"2026-06-08T06:41:41","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=19258"},"modified":"2026-06-08T03:41:44","modified_gmt":"2026-06-08T06:41:44","slug":"single-layer-bordered-prime-magic-square-of-odd-orders","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=19258","title":{"rendered":"Single-Layer Bordered Prime Magic Square of Odd Orders"},"content":{"rendered":"\n

This work brings Bordered Magic Squares of Single Digit or Single Layer or Cocentric Bordered Magic Squares of even orders<\/strong>. By Single Digit <\/strong>or Single Layer<\/strong> or Cocentric Bordered<\/strong> magic squares, we understand that when we remove the upper layer <\/strong>or upper border<\/strong> still we are left with magic squares of lower orders. This work is specially for the prime number entries. It is done for odd orders. For even orders refer the link<\/a>.
Instead of writing from upper to lower orders, we shall write below some examples from lower to upper orders. This means that the lower order magic squares are embedded<\/strong> or nested<\/strong> in the next orders. See below examples starting from magic squares of order 3.<\/p>\n\n\n\n

Cocentric Prime Magic Squares of Odd Orders up to 111<\/h4>\n\n\n\n
Prime Magic Square of Order 3<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Prime Magic Square of Order 5<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 7<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 9<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 11<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 13<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 15<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 17<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 19<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 21<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 23<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 25<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Prime Magic Square of Order 27<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 29<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 31<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 33<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 35<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 37<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 39<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 41<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 43<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 45<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 47<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 49<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
Prime Magic Square of Order 51<\/h5>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n

Due to size of the magic squares, the higher orders are not shown here. They are in txt file given in Zenodo work. See the link below:<\/p>\n\n\n\n

<\/p>\n\n\n\n

References<\/h4>\n\n\n\n
    \n
  1. H. White, Magic Squares of Prime Numbers, https:\/\/budshaw.ca\/PrimeMagicSquares.html<\/a><\/li>\n\n\n\n
  2. Heinz, Harvey “Prime Numbers Magic Squares” http:\/\/recmath.org\/Magic%20Squares\/primesqr.htm<\/a><\/li>\n\n\n\n
  3. Makarova, Natalia “Concentric magic squares of primes”
    http:\/\/primesmagicgames.altervista.org\/wp\/forums\/topic\/concentric-magic-squares-of-primes\/<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    This work brings Bordered Magic Squares of Single Digit or Single Layer or Cocentric Bordered Magic Squares of even orders. By Single Digit or Single Layer or Cocentric Bordered magic squares, we understand that when we remove the upper layer or upper border still we are left with magic squares of lower orders. This work […]<\/p>\n","protected":false},"author":1,"featured_media":19270,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[3],"tags":[],"class_list":["post-19258","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-magic-squares"],"jetpack_featured_media_url":"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/19x19c.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/19258","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=19258"}],"version-history":[{"count":1,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/19258\/revisions"}],"predecessor-version":[{"id":19289,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/19258\/revisions\/19289"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/19270"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=19258"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=19258"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=19258"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}