Thread: Prime Magic Square

Hello.

Wondering if anyone has a link or a solution to this problem, its from David Wells` Penguin Dictionary of Curious and Interesting Numbers...(from the entry on the number 144)

The smallest magic square composed of consecutive primes comprises the 144 odd primes from 3 upwards. The magic constant is 4515.

Ive tried searching online for this magic square but can`t find it anywhere, does anyone have a web link or a solution to it?. (I would like to make the square and use it for music possibly, 12 squared is a good number/concept for music).

Ive tried looking at various methods for constructing magic squares but they all seem to apply to sequential numbers, I am guessing making squares of consecutive primes is more difficult?

Thanks in advance for any info/advice.

Originally Posted by MusicMathsEtc

Hello.

Wondering if anyone has a link or a solution to this problem, its from David Wells` Penguin Dictionary of Curious and Interesting Numbers...(from the entry on the number 144)
Ive tried searching online for this magic square but can`t find it anywhere, does anyone have a web link or a solution to it?. (I would like to make the square and use it for music possibly, 12 squared is a good number/concept for music).

Ive tried looking at various methods for constructing magic squares but they all seem to apply to sequential numbers, I am guessing making squares of consecutive primes is more difficult?

Thanks in advance for any info/advice.

What about the magic squares in this link: Prime Magic Squares .......? They're all smaller than 12 x 12 .....!!

The link Prime Magic Square -- from Wolfram MathWorld has the 12 x 12 magic square you ask about. But ...... What David Wells said is wrong. The entry should read: The smallest magic square composed of consecutive primes and including the number 1 comprises the 143 odd primes from 3 upwards. The magic constant is 4514.

Thanks very much, no wonder I couldnt find the square Wells talks about (slightly annoying that it is wrong, makes me wonder about the rest of the book), that Wolfram square will do nicely (12x12=144 numbers, 144 is a fibonacci number which works well for music, 12 notes in the chromatic scale, the constant 4,5,1,4 and its inversion 8,7,11,8 are both harmonic minor subsets, gives plenty of options)