20070504, 12:46  #1 
(loop (#_fork))
Feb 2006
Cambridge, England
13×491 Posts 
Prime cubes!
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 backbottomright 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. 
20070504, 14:00  #2 
(loop (#_fork))
Feb 2006
Cambridge, England
18EF_{16} Posts 
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 dimension5 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 
20070504, 14:10  #3 
Jan 2005
Transdniestr
503 Posts 
Cool beans, fivemack

20070505, 01:37  #4 
"Jason Goatcher"
Mar 2005
110110110011_{2} Posts 
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. :) 
20070704, 00:18  #5 
Jan 2005
Transdniestr
503 Posts 
This thread is the inspiration for pp407 this week at www.primepuzzles.net
Last fiddled with by grandpascorpion on 20070704 at 00:21 
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