Prime cubes!

[fivemack]

123401 + 90*x + 31590*y + 42126*z is prime for x,y,z = 0..2

58031 + 180*x + 11286*y + 52290*z has the same property and a smaller back-bottom-right value; 22123 + 330*x + 26550*y + 26880*z also has the same property, but is spoiled because there are some duplicates in the cube.

17033 + 1254x + 6630y + 47250z has BBR 127301 and no duplicates.

Code is below, it's pretty obvious ... same as the squares search to get planes, file by [dx,dy], then look for planes with the same dx and dy and with starts in arithmetic progression.

I'd be quite impressed if someone presented a 4^3 prime cube or a 3^4 prime hypercube, though I imagine a 2^4 or even 2^5 prime hypercube wouldn't be impossible.

[fivemack]

And, indeed, by a different route, here's a 2x2x2x2 hypercube

11 17 41 47
31 37 61 67

53 59 83 89
73 79 103 109

The attached code finds 8710 hypercubes with entries all different and <1024.

Extending it in the obvious way finds 329 dimension-5 objects with entries all different and <4096, of which the smallest largest entry is 1217, from

43 + 66x + 120y + 270z + 340w + 378t are all distinct and prime for [x,y,z,w,t] in [0,1]^5

likewise 7 + 10x + 66y + 234z + 570w + 846t

[grandpascorpion]

Cool beans, fivemack

[jasong]

I've JUST NOW figured out what the heck is going on in this thread.

Apparently the fact that I scored a 140 IQ on a math test in the 9th grade doesn't amount to a hill of beans in reality. Oh, well, since I've always credited my good qualities to my parents and Jesus, I'm not going to fret over it. :)

[grandpascorpion]

This thread is the inspiration for pp407 this week at www.primepuzzles.net