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Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
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This was said to be unsolvable by a no less eminent scientist than G.B. F. Riemann. However, if ordered sets of the prime sequence are set out as another sequence:
[3, 5, 7,  15], [5, 7, 11,  23], [7, 11, 13,  31], ... and these sets are treated as points in a four dimensional hyperspace, then the sequence becomes a polygonal arc in 4D. Using linear algebra, finding the direction ratios and intercepts of the line segments produced of the arc, starting from the first two points provides a means of lowering the dimension of the space by unity at a time, but with no loss of information about the prime sequence. This is because on the axis planes, where intercepts are located, one of the coordinates is zero and the other remaining coordinates become a point in a space of dimension, one less. Finally in 2D space, the intercepts of finite discrete functions of the gradients or higher derivatives might have regularity, or a way of producing regularity might be found. This exercise can be done in any even dimension hyperspace: [4, 6, 8, ... ]
There are four coordinates here because of a constraint, that is the sum of an even number of uneven integers is an even integer [zero included]. The solution to the subject appears to reduce to an exercise in linear algebra and a discrete version of the Legendre transformation.