How Often Will a Great Earthquake Strike India and Its Neighbours? The Exact Discrete b-Value Estimator, Its Error, and Return Periods From 24,325 USGS Events, 1970–2026

The Gutenberg–Richter law says that the number of earthquakes of magnitude at least m falls by a factor of 10^b for each unit of magnitude. The b-value fixes how often large events occur and is an input to seismic hazard for structural design. Using the USGS ComCat catalogue for the region 6–38°N, 66–98°E (India, the Himalaya, the Hindu Kush, Myanmar and neighbours), I study 24,325 events of magnitude 4 or more from 1970-02-12 to 2026-10-20. I derive the exact maximum-likelihood b for magnitudes reported to 0.1 units, show that the widely used Aki–Utsu formula is its approximation with relative error −u²/12 + u³/12 + O(u⁴), and give the delta-method variance of an extrapolated rate. With all magnitude types, 1990–2026 and completeness magnitude 4.4, b = 1.1482 (bootstrap s.e. 0.0108; 11,712 events). That estimate is dominated by body-wave magnitudes, which saturate for large events. Restricting to moment magnitudes at or above 5.5 gives b = 0.973 (s.e. 0.044; 493 events). The two models imply very different hazard: 0.023 versus 0.049 events of magnitude 8 or more per year, that is, a 69% versus a 92% chance of at least one in 50 years. The moment-magnitude model matches the observed counts at magnitude 6.5–7.5 far better. Annual counts are over-dispersed (index 2.40), which widens the confidence intervals but does not change the conclusion.