Ooops... Rereading the Sayles's article, he found a 6x6 pandiagonal multiplicative square in 1913... With the same set of integers than my first example (and of course the same product 1.02 E+14). My second example has a product 8.58 E+13. Here is a third example with a new better product 2.99 E+12: 5 720 160 45 80 1440 4800 12 150 192 300 6 9 400 288 25 144 800 320 180 10 2880 20 90 75 48 2400 3 1200 96 576 100 18 1600 36 50 It is now the best known square using the smallest product. However its MaxNb 4800 is bigger than the MaxNb 4410 of the second example. Open problems: -Is 2,985,984,000,000 the smallest possible product? -Is 4410 the smallest possible MaxNb? Christian.