In John Colson's annotations of Newton's "The Method of Fluxions", page 162, we can find an ingenious method to "change Division into Multiplication", where "every Operation will at least double the number of Figures found by the preceding Operation". Could William Shanks be using such method for his reciprocal of primes? Reference: https://archive.org/details/methodoffluxions00newt/page/162/mode/2up
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