Riffs and Rotes • Happy New Year 2025

Posted on January 1, 2025 by Jon Awbrey

\text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}.

\text{Then} ~ 2025 = 81 \cdot 25 = 3^4 5^2 = {p_2}^4 {p_3}^2 = {p_2}^{{p_1}^{p_1}} {p_3}^{p_1} = {p_{p_1}}^{{p_1}^{p_1}} {p_{p_2}}^{p_1} = {p_{p_1}}^{{p_1}^{p_1}} {p_{p_{p_1}}}^{p_1}

No information is lost by dropping the terminal 1s.  Thus we may write the following form.

2025 = {p_p}^{p^p} {p_{p_p}}^p

The article linked below tells how forms of that sort correspond to a family of digraphs called riffs and a family of graphs called rotes.  The riff and rote for 2025 are shown in the next two Figures.

Riff 2025

Riff 2025

Rote 2025

Rote 2025

Reference

cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate

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