This work is also available online at the following link:<\/p>\n\n\n\n
Prime Magic Squares of Order 15<\/h4>\n\n\n\n
Below are few examples of prime magic squares of order 15 with different representations<\/strong>.<\/p>\n\n\n\n It is block-bordered prime magic square of order 15<\/strong>. It is composed of different sums prime magic squares of order 3. <\/strong>See below few examples of order 3×3:<\/p>\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square of order 15<\/strong>. It is composed of equal sums<\/strong> prime magic squares of order 3. <\/strong>See below few examples of order 3×3:<\/p>\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square of order 15<\/strong>. It is composed of different sum<\/strong> cocentric<\/strong> prime magic squares of order 5.<\/strong> It contains prime magic squares of order 3. <\/strong>See below few examples of order 5×5:<\/p>\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square of order 15<\/strong>. It is composed of equal sums<\/strong> cocentric<\/strong> prime magic squares of order 5.<\/strong> It contains prime magic squares of order 3. <\/strong>See below few examples of orders 5 and 3:<\/p>\n\n\n <\/p>\n\n\n\n It is cocentric single-layer bordered prime magic square of order 15<\/strong>. the internal layer are also prime magic squares of orders 13, 11, 9, 7, 5 and 3. See below:<\/p>\n\n\n <\/p>\n\n\n\n Below are few examples of prime magic squares of order 16 with different representations<\/strong>.<\/p>\n\n\n\n It is block-bordered prime magic square of order 16<\/strong>. The internal blocks are different sums prime magic square of order 4. <\/strong>See below few examples of order 4:<\/p>\n\n\n\n <\/p>\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square of order 16<\/strong>. The internal blocks are equal sums prime magic square of order 4. <\/strong>See below few examples of order 4:<\/p>\n\n\n\n <\/p>\n\n\n <\/p>\n\n\n\n <\/p>\n\n\n <\/p>\n\n\n\n t is cocentric single-layer bordered prime magic square of order 16<\/strong>. the internal layer are also prime magic squares of orders 14, 12, 10, 8, 6 and 4. The orders 4 to 14 is given before in another part on prime magic squares of order 14.<\/p>\n\n\n\n <\/p>\n\n\n\n Below are few examples of prime magic squares of order 17 with different representations<\/strong>.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square of order 17 <\/strong>embedded with a prime magic square of order 15 <\/strong>with different sums prime magic squares of order 3<\/strong>. The prime magic square of order 15<\/strong> is the same as given in section on prime magic squares of order 15.<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square of order 17 <\/strong>embedded with a prime magic square of order 15 <\/strong>with equal sums prime magic squares of order 3<\/strong>. The prime magic square of order 15<\/strong> is the same as given in section on prime magic squares of order 15.<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square of order 17 <\/strong>embedded with a prime magic square of order 15 <\/strong>with different sums cocentric prime magic squares of order 5<\/strong>. The prime magic square of order 15<\/strong> is the same as given in section on prime magic squares of order 15.<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square of order 17 <\/strong>embedded with a prime magic square of order 15 <\/strong>with equal sums cocentric prime magic squares of order 5<\/strong>. The prime magic square of order 15<\/strong> is the same as given in section on prime magic squares of order 15.<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n It is cocentric single-layer bordered prime magic square of order 17<\/strong>. the internal layer are also prime magic squares of orders 15, 13, 11, 9, 7, 5 and 3. It is the same as given in section on prime magic square of order 15,<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n Below are few examples of prime magic squares of order 18 with different representations<\/strong>.<\/p>\n\n\n\n It is block-structured prime magic square of order 18<\/strong>. The internal blocks are different sums prime magic squares of order 3. <\/strong>See below few examples of order 3:<\/p>\n\n\n\n <\/p>\n\n\n <\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 18<\/strong>. The internal blocks are equal sums prime magic squares of order 3. <\/strong>See below few examples of order 3:<\/p>\n\n\n\n <\/p>\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 18<\/strong>. The internal blocks are different sums cocentric prime magic squares of order 6. <\/strong>See below few examples:<\/p>\n\n\n\n <\/p>\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 18<\/strong>. The internal blocks are four equal sums<\/strong> prime magic squares of order 9. <\/strong>These are again composed of different sums prime magic squares oforder 3. <\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 18<\/strong>. The internal blocks are four equal sums cocentric prime magic squares of order 9. <\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n It is cocentric single-layer bordered prime magic square of order 18.<\/strong> The internal part of order 16 is the same as given above in the section of prime magic square of order 16.<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n Below are few examples of prime magic squares of order 19 with different representations<\/strong>.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square of order 19 <\/strong>embedded with a prime magic square of order 15 <\/strong>with different sums prime magic squares of order 3<\/strong>. The prime magic square of order 15<\/strong> is the same as given in section on prime magic squares of order 15.<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square of order 19 <\/strong>embedded with a prime magic square of order 15 <\/strong>with equal sums prime magic squares of order 3<\/strong>. The prime magic square of order 15<\/strong> is the same as given in section on prime magic squares of order 15.<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square of order 19 <\/strong>embedded with a prime magic square of order 15 <\/strong>with different sums cocentric prime magic squares of order 5<\/strong>. The prime magic square of order 15<\/strong> is the same as given in section on prime magic squares of order 15.<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square of order 19 <\/strong>embedded with a prime magic square of order 15 <\/strong>with equal sums cocentric prime magic squares of order 5<\/strong>. The prime magic square of order 15<\/strong> is the same as given in section on prime magic squares of order 15.<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n It is cocentric single-layer bordered prime magic square of order 19<\/strong>. the internal layer are also prime magic squares of orders 17, 15, 13, 11, 9, 7, 5 and 3. It is the same as given in section on prime magic square of order 17,<\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n Below are few examples of prime magic squares of order 20 with different representations<\/strong>.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 20<\/strong>. The internal blocks are different sums prime magic squares of order 3. <\/strong>See below few examples of order 4:<\/p>\n\n\n\n <\/p>\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 20<\/strong>. The internal blocks are equal sums prime magic squares of order 4. <\/strong>See below few examples of order 4:<\/p>\n\n\n\n <\/p>\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 20<\/strong>. The internal blocks are different sums cocentric prime magic squares of order 5. <\/strong>See below few examples:<\/p>\n\n\n\n <\/p>\n\n\nExample 1. Different Sums Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/15x15-3x3b-1.png\")
<\/figure>\n<\/div>\n\n\n![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/15x153x3b-1.png\")
<\/figure>\n<\/div>\n\n\nExample 2. Equal Sums Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/15x15-3x3e-2.png\")
<\/figure>\n<\/div>\n\n\n![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/15x153x3e-2.png\")
<\/figure>\n<\/div>\n\n\nExample 3. Different Sums Blocks of Cocentric Prime Magic Squares of Order 5<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/15x15-5x5b-3.png\")
<\/figure>\n<\/div>\n\n\n![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/15x155x5b-3.png\")
<\/figure>\n<\/div>\n\n\nExample 4. Equal Sums Blocks of Cocentric Prime Magic Squares of Order 5<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/15x15-5x5e-4.png\")
<\/figure>\n<\/div>\n\n\n![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/15x155x5e-4.png\")
<\/figure>\n<\/div>\n\n\nExample 5. Cocentric Single-Layer Bordered Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/15x15c-5.png\")
<\/figure>\n<\/div>\n\n\n![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/15x1513119753c-5-scaled.png\")
<\/figure>\n<\/div>\n\n\nPrime Magic Squares of Order 16<\/h4>\n\n\n\n
Example 1. Different Sums Prime Magic Squares of Order 4<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/16x16b-1.png\")
<\/figure>\n<\/div>\n\n\n![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/16x164x4b-1.png\")
<\/figure>\n<\/div>\n\n\nExample 2. Equal Sums Prime Magic Squares of Order 4<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/16x16e-2.png\")
<\/figure>\n<\/div>\n\n\n![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/16x164x4e-2.png\")
<\/figure>\n<\/div>\n\n\nExample 3: Equal Sums Concentric Prime Magic Squares of Order 8<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/16x16-8x8e-3.png\")
<\/figure>\n<\/div>\n\n\n![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/16x168x8e-3.png\")
<\/figure>\n<\/div>\n\n\nExample 4. Concentric Single-Layer Prime Magic Squares<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/16x16c-4.png\")
<\/figure>\n<\/div>\n\n\nPrime Magic Squares of Order 17<\/h4>\n\n\n\n
Example 1. Block-Bordered Nested with Different Sums Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/17x17-3x3b-1.png\")
<\/figure>\n<\/div>\n\n\nExample 2. Block-Bordered Nested with Equal Sums Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/17x17-3x3e-4.png\")
<\/figure>\n<\/div>\n\n\nExample 3. Block-Bordered Nested with Different Sums Blocks of Cocentric Blocks of Order 5<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/17x17-5x5b-2.png\")
<\/figure>\n<\/div>\n\n\nExample 4. Block-Bordered Nested with Equal Sums Blocks of Cocentric Blocks of Order 5<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/17x17-5x5b-5.png\")
<\/figure>\n<\/div>\n\n\nExample 5. Concentric Single-Layer Prime Magic Squares<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/17x17c-3.png\")
<\/figure>\n<\/div>\n\n\nPrime Magic Squares of Order 18<\/h4>\n\n\n\n
Example 1. Different Sums Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/18x18-3x3b-1.png\")
<\/figure>\n<\/div>\n\n\n![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/18x183x3b-1.png\")
<\/figure>\n<\/div>\n\n\nExample 2. Equal Sums Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/18x18-3x3e-2.png\")
<\/figure>\n<\/div>\n\n\n![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/18x183x3e-2.png\")
<\/figure>\n<\/div>\n\n\nExample 3. Different Sums Cocentri Blocks of Order 6<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/18x18-6x6b-3.png\")
<\/figure>\n<\/div>\n\n\n![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/18x186x6b-3.png\")
<\/figure>\n<\/div>\n\n\nExample 4. Four Equal Sums Blocks of Order 9 with Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/18x18-9x9-3x3b-4.png\")
<\/figure>\n<\/div>\n\n\nExample 5. Four Equal Sums Cocentric Blocks of Order 9<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/18x18-9x9c-5.png\")
<\/figure>\n<\/div>\n\n\nExample 6. Cocentric Single-Layer Bordered Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/18x18c-6.png\")
<\/figure>\n<\/div>\n\n\nPrime Magic Squares of Order 19<\/h4>\n\n\n\n
Example 1. Block-Bordered Nested with Different Sums Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/19x19-3x3b-1.png\")
<\/figure>\n<\/div>\n\n\nExample 2. Block-Bordered Nested with Equal Sums Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/19x19-3x3e-4.png\")
<\/figure>\n<\/div>\n\n\nExample 3. Block-Bordered Nested with Different Sums Blocks of Cocentric Blocks of Order 5<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/19x19-5x5b-2-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 4. Block-Bordered Nested with Equal Sums Blocks of Cocentric Blocks of Order 5<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/19x19-5x5e-5.png\")
<\/figure>\n<\/div>\n\n\nExample 5. Concentric Single-Layer Prime Magic Squares<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/19x19c-3.png\")
<\/figure>\n<\/div>\n\n\nPrime Magic Squares of Order 20<\/h4>\n\n\n\n
Example 1. Different Sums Blocks of Order 4<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/20x20-4x4b-1.png\")
<\/figure>\n<\/div>\n\n\n![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/20x204x4b-1.png\")
<\/figure>\n<\/div>\n\n\nExample 2. Equal Sums Blocks of Order 4<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/20x20-4x4e-3.png\")
<\/figure>\n<\/div>\n\n\n![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/20x204x4e-3.png\")
<\/figure>\n<\/div>\n\n\nExample 3. Different Sums Cocentric Blocks of Order 5<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/20x20-5x5b-2.png\")
<\/figure>\n<\/div>\n\n\n