Rigorous Numerics & Algorithms
for Prime Calculation OS
Building upon the benchmarks of the 2010s, this report reviews key literature from 2020–2025.
The analysis highlights a 5-year trend focused less on theoretical novelty and more on the "practical application of verified computation" and "extreme optimization of existing methods."
B Current State & Challenges
2025 Summary
Trend: Precision vs Complexity
*Conceptual visualization of progress
∎ Research Position Breakthrough
The preceding studies have established strong benchmarks in their respective fields as follows:
verification per problem
guarantees
FPUs & controllers
for evaluating $\pi(x)$
However, a "Prime Calculation OS" that encapsulates analytic prime formulas within finite operations and a $\Sigma_1$-type ledger has yet to be constructed.
The breakthrough of this research lies in providing the OS structure and the finite closure framework to fill this gap, directly connecting prime calculation to the contexts of verified numerics and formal verification.