Searching For Rh | Counterexamples Вђ” Exploring Data Вђ“ Math В€© Programming

In the article Searching for RH Counterexamples — Exploring Data on the blog Math ∩ Programming , author Jeremy Kun shifts from the engineering challenges of building a distributed search system to analyzing the mathematical patterns within the data collected. The write-up focuses on the following key areas:

: To narrow the search space, the exploration looks for patterns in the prime factorizations of high-performing witness values. This involves jumping ahead in the superabundant number enumeration to specific "level sets" that are more likely to yield extreme values. In the article Searching for RH Counterexamples —

. The search targets "witness values"—ratios of the divisor sum to the upper bound—where a value >1is greater than 1 would disprove RH. Current data suggests that if a counterexample exists,

: The Riemann Hypothesis (RH) is equivalent to Robin’s Inequality, which states that for , the sum of divisors is bounded by it would likely have between 1

: By plotting the best witness values found so far, Kun uses logarithmic models to estimate where a counterexample might actually exist. Current data suggests that if a counterexample exists, it would likely have between 1,000 and 10,000 prime factors .