Editing Magic square (section)

===Extra constraints===
[[File:Magic prime square 12.svg|thumb|Magic square of primes]]
Certain extra restrictions can be imposed on magic squares.

If raising each number to the ''n''th power yields another magic square, the result is a bimagic (n&nbsp;=&nbsp;2), a trimagic (n&nbsp;=&nbsp;3), or, in general, a [[multimagic square]].

A magic square in which the number of letters in the name of each number in the square generates another magic square is called an [[alphamagic square]].

There are magic squares consisting [[prime magic square|entirely of primes]]. [[Rudolf Ondrejka]] (1928–2001) discovered the following 3×3 magic square of [[prime number|primes]], in this case nine [[Chen prime]]s:

{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:7em;height:7em;table-layout:fixed;"
|-
| 17 || 89 || 71
|-
| 113 || 59 || 5
|-
| 47 || 29 || 101
|}

The [[Green–Tao theorem]] implies that there are arbitrarily large magic squares consisting of primes.

The following "reversible magic square" has a magic constant of 264 both upside down and right way up:<ref>Karl Fulves, [http://www.markfarrar.co.uk/othmsq01.htm#reversible Self-working Number Magic (Dover Magic Books)]</ref>
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:8em;height:8em;table-layout:fixed;"
| 96 || 11 || 89 || 68
|-
| 88 || 69 || 91 || 16
|-
| 61 || 86 || 18 || 99
|-
| 19 || 98 || 66 || 81
|}

[[File:Ramanujan_magic_square_construction.svg|thumb|Construction of Ramanujan's magic square from a [[Latin square]] with distinct diagonals and day (D), month (M), century (C) and year (Y) values, and Ramanujan's birthday example]]
When the extra constraint is to display some date, especially a birth date, then such magic squares are called birthday magic square. An early instance of such birthday magic square was created by [[Srinivasa Ramanujan]]. He created a 4×4 square in which he entered his date of birth in D&ndash;M&ndash;C-Y format in the top row and the magic happened with additions and subtractions of numbers in squares. Not only do the rows, columns, and diagonals add up to the same number, but the four corners, the four middle squares (17, 9, 24, 89), the first and last rows two middle numbers (12, 18, 86, 23), and the first and last columns two middle numbers (88, 10, 25, 16) all add up to the sum of 139.