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Old 2007-05-04, 12:46   #1
fivemack
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Feb 2006
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Default 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 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.
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Old 2007-05-04, 14:00   #2
fivemack
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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
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Old 2007-05-04, 14:10   #3
grandpascorpion
 
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Cool beans, fivemack
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Old 2007-05-05, 01:37   #4
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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. :)
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Old 2007-07-04, 00:18   #5
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This thread is the inspiration for pp407 this week at www.primepuzzles.net

Last fiddled with by grandpascorpion on 2007-07-04 at 00:21
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