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Can Prime 521 Weave 520 Chords?
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Can Prime 521 Weave 520 Chords?

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Can one multiplication rule visit every nonzero position around a prime-numbered circle?

Start with 1 and repeatedly multiply the previous result by 3 modulo 521. Because 3 is a primitive root of this prime, the sequence visits all 520 nonzero residues before returning to the start. Placing those results on a circle and connecting consecutive positions produces this dense chord web.

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Music: 'The Challenger' by The Soundlings

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r0=1,rn+1=3rnmod521r₀=1, rₙ₊₁=3rₙ mod 521xn=cos(2πrn/521)xₙ=cos(2πrₙ/521)yn=sin(2πrn/521)yₙ=sin(2πrₙ/521)
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