Prime magic square.

[mfgoode]

Can you give a prime magic square of order 3 with the least constant?

A magic square of order 3 is one which consists of a 3 x 3 grid with 3 rows and 3 columns of numbers in which all the rows, columns and the two diagonals add up to the same number called the magic constant. Try making an ordinary one of the first 9 digits from 1 - 9 (inclusive)
The one I am asking for is to be made up of odd primes as 2 will upset the parity.
Hint: the primes are all below 100.
Mally

[mfgoode]

Its been a week now without a solution. There must be some program to fill up the 9 squares to give a magic constant based only on primes.
Okay! I will release a set of three primes that make up this square.
They may be used to make a column or row as you view it or wish

67 , 1 , 43.

Hint: its not a diagonal.

There are some remarkable properties of magic squares worth studying.

I have evolved a property that could be used for chip circuits in an amazing way.

Will GIMPS protect my rights should I publish it in this forum?

Alternatively, could anyone give me a web site for firms making electronic and chip circuits
where this could be used to advantage?

Thanking you,

Mally

[Kees]

will this do



67 1 43
13 37 61
31 73 7

[Kees]

Or without the 1 (ugly in a prime list)


17 89 71
113 59 5
47 29 101

[mfgoode]

Originally Posted by Kees

Or without the 1 (ugly in a prime list)


17 89 71
113 59 5
47 29 101

:surprised : good going Kees but thats the one with the smallest constant (111).
I believe there is the constant 102 in an order 4 prime magic square but I have not tried it . Maybe you could work it out
Mally

[Kees]

13 43 59 5
23 19 37 41
53 47 17 3
31 11 7 71




no 102 but 120

what do you think of this relation?

1010=10

[mfgoode]

Originally Posted by mfgoode

:surprised : good going Kees but thats the one with the smallest constant (111).
I believe there is the constant 102 in an order 4 prime magic square but I have not tried it . Maybe you could work it out
Mally

:
Thank you Kees. But the lowest constant for distinct primes of order 4 is 102.
This was found by Ernest Bergholt and C.D. Shuldham way back in the early 1900's. Martin Gardner also mentions it. So does Dudeney In his book 'Amusements in Mathematics. I got it on the net from 'The chicago Monist' with the same statement but could not retrieve it for you, the mention, and not the solution

This means that the magic constant from yours (120) is 18 less(102).
If you subtract 6 from each of your numbers leaving say, right most column intact I have come very close to it and all that remains is to fill up the last row. I have tried very hard but cannot make it right.

Maybe it requires different primes from the numbers you have given. Maybe the even prime 2 is also taken into account. I dont know. Even Martin Gardner mentions it but does not provide the solution.

So if you can crack it out you will have a feather in your bonnet!

All the best,

Mally

[ATH]

I don't think there is a solution for 102.

I'm pretty sure I tried all possibilities using primes from 2 to 97 and only once each in a 4x4 square. Closest I got was these 4 using 23 twice in each:

7 31 5 59
29 37 13 23
47 11 41 3
19 23 43 17

7 47 29 19
5 41 13 43
31 11 37 23
59 3 23 17

41 43 5 13
3 17 59 23
47 19 7 29
11 23 31 37

59 31 5 7
3 11 41 47
23 37 13 29
17 23 43 19

[mfgoode]

Thank you ATH for your post.
There are a few order 4 prime magic sqares which have distinct primes and not like yours which use the number 23 twice. I presume you have done this on your own and commend your effort as these squares can be quite mind boggling.
Please refer to Kees's two solutions one with the number 1 now not considered a prime and the other without it. Till the 20th century the number 1 was considered a prime. I have the pros's and con' why this is not so now.
I am presenting a summary from the net given by H. E. Dudeney which gives the order 4 constant as 102. May be its a misprint but that is why I have considered the possibility that the summary is right. It has been mentioned by Martin Gardner also.

The following summary is taken from The Monist (Chicago) for October 1913:—

Order
of Square. Totals
of Series. Lowest
Constants. Squares
made by—
3rd 333 111 Henry E.
Dudeney (1900).
4th 408 102 Ernest Bergholt <<<<<<<<<<< Please note.
and C. D. Shuldham.
5th 1065 213 H. A. Sayles.
6th 2448 408 C. D. Shuldham
and J. N. Muncey.
7th 4893 699 do.
8th 8912 1114 do.
9th 15129 1681 do.
10th 24160 2416 J. N. Muncey.
11th 36095 3355 do.
12th 54168 4514 do.

For further details the reader should consult the article itself, by W. S. Andrews and H. A. Sayles.

Hope this clarifies the problem

Mally

[mfgoode]

Originally Posted by Kees

13 43 59 5
23 19 37 41
53 47 17 3
31 11 7 71




no 102 but 120

what do you think of this relation?

1010=10

Is it number 10 in binary equal to 10 in decimal?
Mally

[xilman]

Originally Posted by Kees

what do you think of this relation?

1010=10

I think that you like radix 3 and radix 30 (with those values in decimal, of course).


Paul