Here we analyze the pair entropy function on large numbers by generating sets of pseudo-random numbers and calculating the pair entropy as a function of number of digits. We analyze the statistical behavior of the average entropy, determine that the average entropy grows logarithmically in the asymptotic limit, and discuss the behavior of higher statistical moments. We observe several distinct regions emerge with transitions that depend on the base of the numbers considered.

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[1] William Julius, "Pair Entropy Data for Long Numbers", IEEE Dataport, 2024. [Online]. Available: http://dx.doi.org/10.21227/9pp4-1297. Accessed: Apr. 24, 2024.
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doi = {10.21227/9pp4-1297},
url = {http://dx.doi.org/10.21227/9pp4-1297},
author = {William Julius },
publisher = {IEEE Dataport},
title = {Pair Entropy Data for Long Numbers},
year = {2024} }
TY - DATA
T1 - Pair Entropy Data for Long Numbers
AU - William Julius
PY - 2024
PB - IEEE Dataport
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William Julius. (2024). Pair Entropy Data for Long Numbers. IEEE Dataport. http://dx.doi.org/10.21227/9pp4-1297
William Julius, 2024. Pair Entropy Data for Long Numbers. Available at: http://dx.doi.org/10.21227/9pp4-1297.
William Julius. (2024). "Pair Entropy Data for Long Numbers." Web.
1. William Julius. Pair Entropy Data for Long Numbers [Internet]. IEEE Dataport; 2024. Available from : http://dx.doi.org/10.21227/9pp4-1297
William Julius. "Pair Entropy Data for Long Numbers." doi: 10.21227/9pp4-1297