Correlation in Number Theory, Part II: From Pearson to Prime Gaps

Welcome back to Part II of our exploration of correlation in number theory. We survey how linear and rank correlations — from Pearson’s product-moment coefficient to Spearman and Kendall — reveal hidden order among numbers, even when relationships aren’t simple. Tracing ideas from Galton to Pearson, we discuss how correlations can illuminate patterns in primes and prime gaps, and connect these ideas to statistical mechanics through correlation functions and Onsager’s regression hypothesis. We also flag the limits: correlation does not imply causation. A friendly, accessible tour with concrete number-theory examples and a look ahead to future directions.

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