This work is also available online at the following link:<\/p>\n\n\n\n
Prime Magic Squares of Order 27<\/h4>\n\n\n\n
Below are few examples of prime magic squares <\/strong>of order 27 with different representations. We know that 27=33<\/sup> . It means that most of the blocks are composition prime magic squares of order 3 and 9<\/p>\n\n\n\n It is block-structured prime magic square of order 27<\/strong>. It is composed of different sums<\/strong> prime magic squares of order 3.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 27<\/strong>. It is composed of equal sums<\/strong> prime magic squares of order 3. In order to bring these equal sums<\/strong> we used the idea of fixed prime 1000003 in middle of each block of order 3. All other primes are distinct.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 27<\/strong>. It is composed of different sums cocentric prime magic squares<\/strong> of order 9. The intenal blocks of orders 7, 5 and 3 are also of different sums<\/strong> magic squares.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 27<\/strong>. It is composed of equal sums cocentric prime magic squares<\/strong> of order 9. The intenal blocks of orders 7, 5 and 3 are also of different sums<\/strong> magic squares.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 27<\/strong>. It is composed of different sums<\/strong> prime magic square of order 9. Each block of order 9 is again formed by 9 different sum prime magic squares.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 27<\/strong>. It is composed of equal sums<\/strong> prime magic square of order 9. Each block of order 9 is again formed by 9 equal sums<\/strong> prime magic squares.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n\n\n\n It is concentric single-layer bordered prime magic square<\/strong> of order 27. The internal blocks of orders 25, 23, …., 3 are also prime magic squares studied in the previous work.<\/p>\n\n\n\n <\/p>\n\n\n\n Below are few examples of prime magic squares<\/strong> of order 28 with different representations. We know that 28=4×7. It means that most of the blocks are composition of prime magic squares<\/strong> of orders 4 and 7.<\/p>\n\n\n\n It is block-structured prime magic square<\/strong> of order 28. It is composed of different sums prime magic squares<\/strong> of order 4. <\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square<\/strong> of order 28. It is composed of equal sums prime magic squares<\/strong> of order 4. <\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square<\/strong> of order 28. It is composed of different sums prime magic squares<\/strong> of order 7. <\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured concentric prime magic square<\/strong> of order 28. It is composed of differnt sums prime magic squares<\/strong> of order 7. The internal blocks of orders 5 and 3 are also of different sums<\/strong>.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured concentric prime magic square<\/strong> of order 28. It is composed of equal sums prime magic squares<\/strong> of order 7. The internal blocks of orders 5 and 3 are also of equal sums<\/strong>. It has repeated prime number 1000003 in the middle of each block. All other primes are distinct.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square<\/strong> of order 28. It is composed of four equal<\/strong> sums prime magic squares<\/strong> of order 14. Again each block of order 14 is embedded with different sums <\/strong>prime magic squares of order 3 composing a prime magic square of order 12.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square<\/strong> of order 28. It is composed of four equal sums prime magic squares<\/strong> of order 14. Again each block of order 14 is embedded with equal sums<\/strong> prime magic squares of order 3 composing a prime magic square of order 12.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square<\/strong> of order 28. It is composed of four equal sums prime magic squares<\/strong> of order 14. Again each block of order 14 is embedded with diferent sums<\/strong> prime magic squares of order 4 composing a prime magic square of order 12.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square<\/strong> of order 28. It is composed of four equal sums prime magic squares<\/strong> of order 14. Again each block of order 14 is embedded with equal sums<\/strong> prime magic squares of order 4 composing a prime magic square of order 12.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square<\/strong> of order 28. It is composed of four equal sums prime magic squares<\/strong> of order 14. Again each block of order 14 is embedded with equal sums<\/strong> prime magic squares of order 6 composing a prime magic square of order 12.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square<\/strong> of order 28. It is composed of four equal sums prime magic squares<\/strong> of order 14. Again each block of order 14 is a concentric single-layer prime magic squares. The internal blocks of order 12,10, 8, 6 and 4 are also prime magic squares.<\/p>\n\n\n\n <\/p>\n\n\n\n It is concentric single-layer bordered prime magic square of order 28<\/strong>. The internal block of order 26 is also a concentric single-layer bordered prime magic square<\/strong> as studied in the previous work.<\/p>\n\n\n\n <\/p>\n\n\n\n Below are few examples of prime magic squares of order 29 with different representations.<\/p>\n\n\n\n It is block-bordered prime magic square<\/strong> of order 29. It is composed of nine different sums prime magic squares<\/strong> of order 9 forming a prime magic square of order 27. These are again composed of different sums<\/strong> prime magic squares of order 3.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square<\/strong> of order 29. It is composed of nine different sums concentric single-layer prime magic squares<\/strong> of order 9 forming a prime magic square of order 27. <\/p>\n\n\n\n <\/p>\n\n\n\n It is concentric single-layer bordered prime magic square of order 29<\/strong>. The internal blocks of orders 27 is also a concentric single-layer bordered prime magic square<\/strong> studied in the first section.<\/p>\n\n\n\n <\/p>\n\n\n\n Below are few examples of prime magic squares of order 30 with different representations.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 30<\/strong> composed of different sums<\/strong> prime magic squares of order 30<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 30<\/strong> composed of equal sums<\/strong> prime magic squares of order 3. The blocks of order 3 are composed with a repeated prime number 1000003. This constant helps in bringing equal sums<\/strong> prime magic squares of order 3.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 30<\/strong> composed of different sums<\/strong> prime magic squares of order 5<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 30<\/strong> composed of different sums<\/strong> prime magic squares of order 5. The blocks of order 5 are again composed with inner part as prime magic squares of order 3 of different sums.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 30<\/strong> composed of equal sums<\/strong> prime magic squares of order 5. The blocks of order 5 are again composed with inner part as prime magic squares of order 3 of equal sums.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 30<\/strong> composed of different sums<\/strong> prime magic squares of order 6. The blocks of order 6 are again composed with inner part as prime magic squares of order 4 of different sums<\/strong>.<\/p>\n\n\n\n It is block-structured prime magic square of order 30<\/strong> composed of equal sums<\/strong> prime magic squares of order 6. The blocks of order 6 are again composed with inner part as prime magic squares of order 4 of equal sums.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 30<\/strong> composed of different sums<\/strong> prime magic squares of order 10<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 30<\/strong> composed of different sums<\/strong> prime magic squares of order 10. The blocks of order 10 are a concentric single-layer <\/strong>prime magic square of order 10.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 30<\/strong> composed of equal sums<\/strong> prime magic squares of order 10. The blocks of order 10 are a concentric single-layer <\/strong>prime magic square of order 10.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 30<\/strong> composed of equal sums<\/strong> prime magic squares of order 10. The blcoks of order 10 block-borderd with inner part as equal sums prime magic squares of order 4 formng magic squares of order 8.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-structured prime magic square of order 30<\/strong> composed of four equal sums concentric single-layer prime magic squares <\/strong>of order 15<\/p>\n\n\n\n <\/p>\n\n\n\n It is cocentric single-layer bordered prime magic square of order 30<\/strong>. The internal prime magic squares of orders 28 is also single-layer bordered<\/strong> prime magic square of order 28 as studied above.<\/p>\n\n\n\n <\/p>\n\n\n\n Below are few examples of prime magic squares of order 31 with different representations.<\/p>\n\n\n\n <\/p>\n\n\n\n It is block-bordered prime magic square<\/strong> of order 31. It is composed of nine different sums prime squares<\/strong> of order 9 forming a prime magic square of order 27. Each block of order 9 is again composed of 9 different sums prime magic squares of order 3.<\/p>\n\n\n\n <\/p>\n\n\n\nExample 1. (27-3d) Different Sums Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/27-3d-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 2. (27-3e) Equal Sums Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/27-3e-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 3. (27-9cd) Different Sums Cocentric Prime Magic Squares<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/27-9cd-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 4. (27-9ce) Equal Sums Cocentric Prime Magic Squares<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/27-9ce-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 5.27- (9d-3d) Block-Structured Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/27-9d-3d.png\")
<\/figure>\n<\/div>\n\n\nExample 6. (27-9e-3d) Block-Structured Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/27-9e-3-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 7. 27c Concentric Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/27c-scaled.png\")
<\/figure>\n<\/div>\n\n\nPrime Magic Squares of Order 28<\/h4>\n\n\n\n
Example 8. 28-4d-1. Different Sums Blocks of Order 4<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/28-4d-1-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 9. 28-4e-1. Equal Blocks of Order 4<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/28-4e-1-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 12. 28-7d-1. Blocks of Prime Magic Squares<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/28-7d-1-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 10. 28-7cd-1. Blocks of Concentric Prime Magic Squares<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/28-7cd-1-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 11. 28-7ce-1 Blocks of Concentric Prime Magic Squares<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/28-7ce-1-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 13. 28-14-12-3d. Block-Structured Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/28-14-12-3d-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 14. 28-14-12-3e. Block-Structured Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/28-14-12-3e-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 15. 28-14-12-4d. Block-Structured Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/28-14-12-4d-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 16. 28-14-12-4e. Block-Structured Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/28-14-12-4e-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 17. 28-14-12-6e. Block-Structured Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/28-14-12-6e-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 18. 28-14ce-1. Block-Structured Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/28-14ce-1-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 19. 28c-1. Concentric Single-Layer Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/28c-1-scaled.png\")
<\/figure>\n<\/div>\n\n\nPrime Magic Squares of Order 29<\/h4>\n\n\n\n
Example 20. 29-27-9d. Block-Bordered Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/29-27-9d.png\")
<\/figure>\n<\/div>\n\n\nExample 21. 29-27-9cd. Block-Bordered Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/29-27-9cd-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 22. 29c. Concentric Single-Layer Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/29c-scaled.png\")
<\/figure>\n<\/div>\n\n\nPrime Magic Squares of Order 30<\/h4>\n\n\n\n
Example 23. 30-3d. Different Sums Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/30-3d-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 24. 30-3e. Equal Sums Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/30-3e-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 25. 30-5d. Different Sums Blocks of Order 5<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/30-5d-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 26. 30-5cd. Different Sums Blocks of Order 5<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/30-5cd-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 27. 30-5ce. Equal Sums Blocks of Order 5<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/30-5ce-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 28. 30-6cd. Different Sums Blocks of Order 6<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/30-6cd-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 29. 30-6ce. Equal Sums Blocks of Order 3<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/30-6ce-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 30. 30-10d. Different Sums Blocks of Order 10<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/30-10d-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 31. 30-10cd. Different Sums Blocks of Order 10<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/30-10cd-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 32. 30-10ce. Equal Sums Blocks of Order 10<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/30-10ce-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 33. 30-10e-8e-4e. Equal Sums Blocks of Order 10<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/30-10e-8e-4e-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 34. 30-15ce. Equal Sums Blocks of Order 15<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/30-15ce-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 35. 30c. Concentric Single-Layer Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/30c-scaled.png\")
<\/figure>\n<\/div>\n\n\nPrime Magic Squares of Order 31<\/h4>\n\n\n\n
Example 36. 31-29-27-9d. Block-Bordered Prime Magic Square<\/h4>\n\n\n
![\"\"](\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2026\/06\/31-29-27-9d-scaled.png\")
<\/figure>\n<\/div>\n\n\nExample 37. 31-29-27-9cd. Block-Bordered Prime Magic Square<\/h4>\n\n\n