answering my own question
and one obvious question: are you sure that no bimagic square of primes can exist with 121 consecutive primes starting from 3? ;-)
Ok, it canNOT exist: Of course two necessary conditions to hold are order divides Sum[Prime[n],{n,2,order^2+1}] order divides Sum[Prime[n]^2,{n,2,order^2+1}] (here the sum is over the first order^2 odd primes). this does not hold for 11, but even more: besides order = 1 and 2 it does NOT hold for any order <= 5000, interesting. The first condition is however satisfied for order=1,2,12,35,215,225,398,2097,... (tested up to 5000). BTW: this sequence is not in the OEIS... The 2nd is true for order=1,2,4,8,14,16,32,44,172,173,344,430,712,944,2744,... (tested up to 8144), strange 44, isn't it: 44+300,900,2700, but not 8144! again the sequence is not in the OEIS... Christoph