Puzzle 80.- Twin primes - magic squares

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Puzzle 80.- Twin primes - magic squares

Days ago Luis Rodríguez from Venezuela mentioned in an email (19/01/2000) the "twin primes - 3x3 magic squares" (the corresponding cells contain twin primes). According to his note he knew since many years ago one example, other was sent to him by Lee Sallows and other 10 by Mutsumi Suzuki.

As a matter of fact, they are not hard to get. According to a code I made on purpose, the smallest ever possible is this couple:

239	17	191		241	19	193
101	149	197	Twins	103	151	199
107	281	59	Smallest	109	283	61

after which there comes hundreds of them...

Some conspicuous I produced are ending with the same digit, by example:

7457	227	4787		7459	229	4789
1487	4157	6827	Twins	1489	4159	6829
3527	8087	857	same ending digit	3529	8089	859

My largest one (inside the capabilities of the prm function of Ubasic) is this couple :

161879	96221	145007		161881	96223	145009
117497	134369	151241	Twins	117499	134371	151243
123731	172519	106859	my largest	123733	172519	106861

Other curios couple of magic squares that I searched, for is this one:

219829	19309	136849	Twins +10 type	219839	19319	136859
42349	125329	208309	Consecutives	42359	125339	208319
113809	231349	30829	all ending in "9"	113819	231359	30839

Questions:

a) Can you get a twin primes - 3x3 magic square having the least prime K digits, for K= 8, 10 & 12?
b) Can you get a twin M x M magic square for M = 4, 5, 6, ...?

Solutions

John E. Everett, from Waynesboro, VA has sent (24/03/2000) the following twin 4x4 example:

(the lower twin)

101	4229	8837	1229
3461	5477	3581	1877
4637	3389	1949	4421
6197	1301	29	6869

***

John has also sent the remarkable 4x4 prime matrix A, such that B =A+2 (his prime upper twin) & C =A+B+1 is also a prime 4x4 magic square!!!... here is this formidable A magic square:

197	4157	7559	2549
4799	6359	3167	137
4049	3329	1607	5477
5417	617	2129	6299

***

Sudipta Das sent (3/12/2001) the following interesting result

A
209977   353011   326539                 
413071   296509   179947
266479   240007   383041                  
B
209987   353021   326549
413081   296519   179957
266489   240017   383051
C
210019   353053   326581
413113   296551   179989
266527   240049   383083

B = A + 10
C = B + 32

All the elements of A , B and C are primes . 
Also , the middle numbers , i.e. 296509 , 296519 , 296551 are consecutive
primes .

***

Sudipta Das also found (23/1/2002)one solution to question a) K=8:

The smallest 3 X 3 twin magic squares whose least prime is 8 digits long :

( the lower twin )

10308929       10063721       10188467

10066577       10187039       10307501

10185611       10310357       10065149

and also this one:

The smallest 3 X 3 twin magic squares whose least prime is 10 digits long :

( the lower twin )

1001994911      1000075187      1001367329

1000518227      1001145809      1001773391

1000924289      1002216431      1000296707

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