An Avenue Of Advancement In Computing The Distribution Of Primes

The predictively decreasing count of prime occurrences in 2^32 bands of the following thresholds introduces a question. “Can they serve as the basis for a mathematical model defining an FFT?”

Totals

Intermediate Boundary Sub-Totals

We could then take an interest in the viability of extrapolating predictively, and the accuracy of the associated FFT, when evaluated in the context of more or less initial data.

We can develop specific calculations to check results with unexpected certainty. We can run security researcher Bruce Schneier’s definitive “isPrime,” introducing a table of all primes < sqrt(range max value) taken from a table of primes < 2^32, for input data.

As a practical matter, 80,000 entries will do to check an arbitrary start point for a range with a surprisingly large integer max-value.

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