Regarding New Madrid quakes, I read somewhere that large ones occur about every 200 years, but really big ones about every 400 years. Wish I could remember the source. Meanwhile, Venezuela had a really big one in 1812 that killed 20,000 people mostly around Caracas. And 2 more really big quakes at New Madrid also occurred the first half of that year.
The articles @ Wikipedia on the New Madrid Quakes, and the New Madrid Seismic, are fairly good. If you want to get into it deeper:
https://earthquake.usgs.gov/aboutus/nepec/reports/NEPEC_NMSZ_expert_panel_report.pdf
VERY roughly, the sequences of big quakes appear to occur in the New Madrid Seismic Area every 600 years or so. The thing to remember is that these occur as clusters of big quakes, with several strong quakes thrown in for good measure. The series in 1811-12 consisted of 4 quakes 7.0 or larger (even by conservative estimates of magnitude), several more in the 6-7 range, over nearly a year-long period, and very numerous quakes below 6.0.
https://earthquake.usgs.gov/earthquakes/events/1811-1812newmadrid/summary.php
It’s no wonder many residents concluded the area was cursed, or if not that, simply uninhabitable, and left!