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In this article, we demonstrate what children's mathematics has taught us about the prime number theorem. We begin with a brief history of the theorem and existing proofs of it, which rely upon long arguments involving complex analysis or arithmetic functions. In developing our own approach to understanding—and possibly proving—the prime number theorem, we rely instead on children's mathematics. Research in mathematics education has demonstrated ways that children construct additive and multiplicative worlds of nested numbers, and it has framed logarithms as mappings between those two worlds. We frame the prime number theorem as such a mapping and furthermore indicate why it is the natural logarithm that appears in the prime number theorem, wherein additive transformations of adding 1 correspond with multiplicative transformations of multiplying by e.