It is kind of interesting, as part of the Prime Tool Kit I created, one feature is the generation of all unique combinations of 3 primes that sum to each prime.
For Prime 863, I took that list of triples and used it to create cubes in the OpenSCAD "Programmers Solid 3D CAD modeller" opensource software.
The toolkit source is available at github.
See my blog entry for more info on the toolkit and its design.
The resulting output was this:
Data / prog here:
for(i = [
[263,293,307], [271,281,311], [269,283,311], [269,281,313], [257,293,313],
[239,311,313], [269,277,317], [263,283,317], [239,307,317], [233,313,317],
[263,269,331], [251,281,331], [239,293,331], [257,269,337], [233,293,337],
[239,277,347], [233,283,347], [223,293,347], [199,317,347], [179,337,347],
[251,263,349], [233,281,349], [197,317,349], [167,347,349], [241,269,353],
[239,271,353], [233,277,353], [229,281,353], [227,283,353], [199,311,353],
[197,313,353], [193,317,353], [179,331,353], [173,337,353], [163,347,353],
[241,263,359], [233,271,359], [227,277,359], [223,281,359], [211,293,359],
[197,307,359], [193,311,359], [191,313,359], [173,331,359], [167,337,359],
[157,347,359], [151,353,359], [239,257,367], [233,263,367], [227,269,367],
[179,317,367], [149,347,367], [137,359,367], [239,251,373], [233,257,373],
[227,263,373], [197,293,373], [179,311,373], [173,317,373], [137,353,373],
[131,359,373], [233,251,379], [227,257,379], [191,293,379], [173,311,379],
[167,317,379], [137,347,379], [131,353,379], [239,241,383], [229,251,383],
[223,257,383], [211,269,383], [199,281,383], [197,283,383], [173,307,383],
[167,313,383], [163,317,383], [149,331,383], [131,349,383], [127,353,383],
[113,367,383], [107,373,383], [101,379,383], [233,241,389], [223,251,389],
[211,263,389], [197,277,389], [193,281,389], [191,283,389], [181,293,389],
[167,307,389], [163,311,389], [157,317,389], [137,337,389], [127,347,389],
[107,367,389], [101,373,389], [227,239,397], [197,269,397], [173,293,397],
[149,317,397], [113,353,397], [107,359,397], [83,383,397], [229,233,401],
[223,239,401], [211,251,401], [199,263,401], [193,269,401], [191,271,401],
[181,281,401], [179,283,401], [151,311,401], [149,313,401], [131,331,401],
[113,349,401], [109,353,401], [103,359,401], [89,373,401], [83,379,401],
[79,383,401], [73,389,401], [197,257,409], [191,263,409], [173,281,409],
[137,317,409], [107,347,409], [101,353,409], [71,383,409], [53,401,409],
[211,233,419], [193,251,419], [181,263,419], [173,271,419], [167,277,419],
[163,281,419], [151,293,419], [137,307,419], [131,313,419], [127,317,419],
[113,331,419], [107,337,419], [97,347,419], [71,373,419], [61,383,419],
[47,397,419], [43,401,419], [191,251,421], [179,263,421], [173,269,421],
[149,293,421], [131,311,421], [89,353,421], [83,359,421], [59,383,421],
[53,389,421], [41,401,421], [23,419,421], [199,233,431], [193,239,431],
[191,241,431], [181,251,431], [163,269,431], [151,281,431], [149,283,431],
[139,293,431], [101,331,431], [83,349,431], [79,353,431], [73,359,431],
[59,373,431], [53,379,431], [43,389,431], [31,401,431], [23,409,431],
[13,419,431], [11,421,431], [197,233,433], [191,239,433], [179,251,433],
[173,257,433], [167,263,433], [149,281,433], [137,293,433], [113,317,433],
[83,347,433], [71,359,433], [47,383,433], [41,389,433], [29,401,433],
[11,419,433], [197,227,439], [191,233,439], [173,251,439], [167,257,439],
[131,293,439], [113,311,439], [107,317,439], [71,353,439], [41,383,439],
[23,401,439], [5,419,439], [3,421,439], [197,223,443], [193,227,443],
[191,229,443], [181,239,443], [179,241,443], [163,257,443], [157,263,443],
[151,269,443], [149,271,443], [139,281,443], [137,283,443], [127,293,443],
[113,307,443], [109,311,443], [107,313,443], [103,317,443], [89,331,443],
[83,337,443], [73,347,443], [71,349,443], [67,353,443], [61,359,443],
[53,367,443], [47,373,443], [41,379,443], [37,383,443], [31,389,443],
[23,397,443], [19,401,443], [11,409,443], [1,419,443], [191,223,449],
[181,233,449], [173,241,449], [163,251,449], [157,257,449], [151,263,449],
[137,277,449], [131,283,449], [107,307,449], [103,311,449], [101,313,449],
[97,317,449], [83,331,449], [67,347,449], [61,353,449], [47,367,449],
[41,373,449], [31,383,449], [17,397,449], [13,401,449], [5,409,449],
[179,227,457], [173,233,457], [167,239,457], [149,257,457], [137,269,457],
[113,293,457], [89,317,457], [59,347,457], [53,353,457], [47,359,457],
[23,383,457], [17,389,457], [5,401,457], [191,211,461], [179,223,461],
[173,229,461], [163,239,461], [151,251,461], [139,263,461], [131,271,461],
[109,293,461], [89,313,461], [71,331,461], [53,349,461], [43,359,461],
[29,373,461], [23,379,461], [19,383,461], [13,389,461], [5,397,461],
[1,401,461], [173,227,463], [167,233,463], [149,251,463], [137,263,463],
[131,269,463], [107,293,463], [89,311,463], [83,317,463], [53,347,463],
[47,353,463], [41,359,463], [17,383,463], [11,389,463], [3,397,463],
[197,199,467], [173,223,467], [167,229,467], [163,233,467], [157,239,467],
[139,257,467], [127,269,467], [113,283,467], [103,293,467], [89,307,467],
[83,313,467], [79,317,467], [59,337,467], [47,349,467], [43,353,467],
[37,359,467], [29,367,467], [23,373,467], [17,379,467], [13,383,467],
[7,389,467], [191,193,479], [173,211,479], [157,227,479], [151,233,479],
[127,257,479], [113,271,479], [107,277,479], [103,281,479], [101,283,479],
[73,311,479], [71,313,479], [67,317,479], [53,331,479], [47,337,479],
[37,347,479], [31,353,479], [17,367,479], [11,373,479], [5,379,479],
[1,383,479], [179,197,487], [149,227,487], [137,239,487], [113,263,487],
[107,269,487], [83,293,487], [59,317,487], [29,347,487], [23,353,487],
[17,359,487], [3,373,487], [181,191,491], [179,193,491], [173,199,491],
[149,223,491], [139,233,491], [131,241,491], [109,263,491], [103,269,491],
[101,271,491], [89,283,491], [79,293,491], [61,311,491], [59,313,491],
[41,331,491], [23,349,491], [19,353,491], [13,359,491], [5,367,491],
[173,191,499], [167,197,499], [137,227,499], [131,233,499], [113,251,499],
[107,257,499], [101,263,499], [83,281,499], [71,293,499], [53,311,499],
[47,317,499], [17,347,499], [11,353,499], [5,359,499], [179,181,503],
[167,193,503], [163,197,503], [149,211,503], [137,223,503], [131,229,503],
[127,233,503], [109,251,503], [103,257,503], [97,263,503], [89,271,503],
[83,277,503], [79,281,503], [67,293,503], [53,307,503], [47,313,503],
[43,317,503], [29,331,503], [23,337,503], [13,347,503], [11,349,503],
[7,353,503], [1,359,503], [173,181,509], [163,191,509], [157,197,509],
[131,223,509], [127,227,509], [113,241,509], [103,251,509], [97,257,509],
[83,271,509], [73,281,509], [71,283,509], [61,293,509], [47,307,509],
[43,311,509], [41,313,509], [37,317,509], [23,331,509], [17,337,509],
[7,347,509], [5,349,509], [1,353,509], [163,179,521], [151,191,521],
[149,193,521], [131,211,521], [113,229,521], [109,233,521], [103,239,521],
[101,241,521], [79,263,521], [73,269,521], [71,271,521], [61,281,521],
[59,283,521], [31,311,521], [29,313,521], [11,331,521], [5,337,521],
[167,173,523], [149,191,523], [113,227,523], [107,233,523], [101,239,523],
[89,251,523], [83,257,523], [71,269,523], [59,281,523], [47,293,523],
[29,311,523], [23,317,523], [3,337,523], [149,173,541], [131,191,541],
[89,233,541], [83,239,541], [71,251,541], [59,263,541], [53,269,541],
[41,281,541], [29,293,541], [11,311,541], [5,317,541], [149,167,547],
[137,179,547], [89,227,547], [83,233,547], [59,257,547], [53,263,547],
[47,269,547], [23,293,547], [5,311,547], [3,313,547], [149,157,557],
[139,167,557], [127,179,557], [113,193,557], [109,197,557], [107,199,557],
[83,223,557], [79,227,557], [73,233,557], [67,239,557], [43,263,557],
[37,269,557], [29,277,557], [23,283,557], [13,293,557], [149,151,563],
[137,163,563], [127,173,563], [109,191,563], [107,193,563], [103,197,563],
[101,199,563], [89,211,563], [73,227,563], [71,229,563], [67,233,563],
[61,239,563], [59,241,563], [43,257,563], [37,263,563], [31,269,563],
[29,271,563], [23,277,563], [19,281,563], [17,283,563], [7,293,563],
[137,157,569], [131,163,569], [127,167,569], [113,181,569], [103,191,569],
[101,193,569], [97,197,569], [83,211,569], [71,223,569], [67,227,569],
[61,233,569], [53,241,569], [43,251,569], [37,257,569], [31,263,569],
[23,271,569], [17,277,569], [13,281,569], [11,283,569], [1,293,569],
[113,179,571], [101,191,571], [59,233,571], [53,239,571], [41,251,571],
[29,263,571], [23,269,571], [11,281,571], [137,149,577], [113,173,577],
[107,179,577], [89,197,577], [59,227,577], [53,233,577], [47,239,577],
[29,257,577], [23,263,577], [17,269,577], [5,281,577], [3,283,577],
[137,139,587], [127,149,587], [113,163,587], [109,167,587], [103,173,587],
[97,179,587], [83,193,587], [79,197,587], [53,223,587], [47,229,587],
[43,233,587], [37,239,587], [19,257,587], [13,263,587], [7,269,587],
[5,271,587], [131,139,593], [113,157,593], [107,163,593], [103,167,593],
[97,173,593], [89,181,593], [79,191,593], [73,197,593], [71,199,593],
[59,211,593], [47,223,593], [43,227,593], [41,229,593], [37,233,593],
[31,239,593], [29,241,593], [19,251,593], [13,257,593], [7,263,593],
[1,269,593], [127,137,599], [113,151,599], [107,157,599], [101,163,599],
[97,167,599], [83,181,599], [73,191,599], [71,193,599], [67,197,599],
[53,211,599], [41,223,599], [37,227,599], [31,233,599], [23,241,599],
[13,251,599], [7,257,599], [1,263,599], [113,149,601], [89,173,601],
[83,179,601], [71,191,601], [29,233,601], [23,239,601], [11,251,601],
[5,257,601], [107,149,607], [89,167,607], [83,173,607], [59,197,607],
[29,227,607], [23,233,607], [17,239,607], [5,251,607], [113,137,613],
[101,149,613], [83,167,613], [71,179,613], [59,191,613], [53,197,613],
[23,227,613], [17,233,613], [11,239,613], [109,137,617], [107,139,617],
[97,149,617], [89,157,617], [83,163,617], [79,167,617], [73,173,617],
[67,179,617], [53,193,617], [47,199,617], [23,223,617], [19,227,617],
[17,229,617], [13,233,617], [7,239,617], [5,241,617], [113,131,619],
[107,137,619], [71,173,619], [53,191,619], [47,197,619], [17,227,619],
[11,233,619], [5,239,619], [3,241,619], [101,131,631], [83,149,631],
[59,173,631], [53,179,631], [41,191,631], [5,227,631], [3,229,631],
[109,113,641], [83,139,641], [73,149,641], [71,151,641], [59,163,641],
[43,179,641], [41,181,641], [31,191,641], [29,193,641], [23,199,641],
[11,211,641], [107,113,643], [89,131,643], [83,137,643], [71,149,643],
[53,167,643], [47,173,643], [41,179,643], [29,191,643], [23,197,643],
[107,109,647], [103,113,647], [89,127,647], [79,137,647], [67,149,647],
[59,157,647], [53,163,647], [43,173,647], [37,179,647], [23,193,647],
[19,197,647], [17,199,647], [5,211,647], [103,107,653], [101,109,653],
[97,113,653], [83,127,653], [79,131,653], [73,137,653], [71,139,653],
[61,149,653], [59,151,653], [53,157,653], [47,163,653], [43,167,653],
[37,173,653], [31,179,653], [29,181,653], [19,191,653], [17,193,653],
[13,197,653], [11,199,653], [101,103,659], [97,107,659], [73,131,659],
[67,137,659], [53,151,659], [47,157,659], [41,163,659], [37,167,659],
[31,173,659], [23,181,659], [13,191,659], [11,193,659], [7,197,659],
[5,199,659], [89,113,661], [71,131,661], [53,149,661], [29,173,661],
[23,179,661], [11,191,661], [5,197,661], [3,199,661], [89,101,673],
[83,107,673], [59,131,673], [53,137,673], [41,149,673], [23,167,673],
[17,173,673], [11,179,673], [89,97,677], [83,103,677], [79,107,677],
[73,113,677], [59,127,677], [47,139,677], [37,149,677], [29,157,677],
[23,163,677], [19,167,677], [13,173,677], [7,179,677], [5,181,677],
[83,97,683], [79,101,683], [73,107,683], [71,109,683], [67,113,683],
[53,127,683], [43,137,683], [41,139,683], [31,149,683], [29,151,683],
[23,157,683], [17,163,683], [13,167,683], [7,173,683], [1,179,683],
[83,89,691], [71,101,691], [59,113,691], [41,131,691], [23,149,691],
[5,167,691], [79,83,701], [73,89,701], [61,101,701], [59,103,701],
[53,109,701], [31,131,701], [23,139,701], [13,149,701], [11,151,701],
[5,157,701], [71,83,709], [53,101,709], [47,107,709], [41,113,709],
[23,131,709], [17,137,709], [5,149,709], [3,151,709], [71,73,719],
[61,83,719], [47,97,719], [43,101,719], [41,103,719], [37,107,719],
[31,113,719], [17,127,719], [13,131,719], [7,137,719], [5,139,719],
[53,83,727], [47,89,727], [29,107,727], [23,113,727], [5,131,727],
[59,71,733], [47,83,733], [41,89,733], [29,101,733], [23,107,733],
[17,113,733], [3,127,733], [53,71,739], [41,83,739], [23,101,739],
[17,107,739], [11,113,739], [59,61,743], [53,67,743], [47,73,743],
[41,79,743], [37,83,743], [31,89,743], [23,97,743], [19,101,743],
[17,103,743], [13,107,743], [11,109,743], [7,113,743], [53,59,751],
[41,71,751], [29,83,751], [23,89,751], [11,101,751], [5,107,751],
[3,109,751], [47,59,757], [23,83,757], [17,89,757], [5,101,757],
[3,103,757], [43,59,761], [41,61,761], [31,71,761], [29,73,761],
[23,79,761], [19,83,761], [13,89,761], [5,97,761], [1,101,761],
[41,53,769], [23,71,769], [11,83,769], [5,89,769], [43,47,773],
[37,53,773], [31,59,773], [29,61,773], [23,67,773], [19,71,773],
[17,73,773], [11,79,773], [7,83,773], [1,89,773], [29,47,787],
[23,53,787], [17,59,787], [5,71,787], [3,73,787], [29,37,797],
[23,43,797], [19,47,797], [13,53,797], [7,59,797], [5,61,797],
[23,31,809], [17,37,809], [13,41,809], [11,43,809], [7,47,809],
[1,53,809], [23,29,811], [11,41,811], [5,47,811], [19,23,821],
[13,29,821], [11,31,821], [5,37,821], [1,41,821], [17,23,823],
[11,29,823], [3,37,823], [17,19,827], [13,23,827], [7,29,827],
[5,31,827], [11,23,829], [5,29,829], [3,31,829], [11,13,839],
[7,17,839], [5,19,839], [1,23,839], [3,7,853], [1,5,857],
[1,3,859]
] )
{
cube(i, center=true);
}
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