Riffs and Rotes • Happy New Year 2025 • https://inquiryintoinquiry.com/2025/01/01/riffs-and-rotes-happy-new-year-20… Let pₙ = the n-th prime. Then 2025 = 81 ∙ 25 = 3⁴ ∙ 5² = (p₂)⁴ ∙ (p₃)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 like this 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 • https://inquiryintoinquiry.files.wordpress.com/2025/01/riff-2025.png Rote 2025 • https://inquiryintoinquiry.files.wordpress.com/2025/01/rote-2025.png Reference — Riffs and Rotes • https://oeis.org/wiki/Riffs_and_Rotes Regards, Jon cc: https://www.academia.edu/community/lnYzY3 cc: https://www.researchgate.net/post/Riffs_and_Rotes_Happy_New_Year_2025