In this article, a case is made for very-large or primary seismogenic structures in convergent margins, based on anomalous large earthquake magnitudes (Mw 8 - 9) relative to rupture lengths. Out of 56,293 earthquakes (magnitudes ≥ 5) cataloged worldwide, the 10 largest events in transform, divergent, and interior settings average magnitudes of 7.3 - 7.6. But in convergent margins, the average magnitude of the 10 largest events is 8.5, roughly 32 times more energy than the other neotectonic settings. The large anomalous magnitudes of energy release in convergent margins are attributed to the transfer of inter-plate stress to the upper-plate, where convergent elastic strain is accumulated during interseismic intervals. The large volumes of rock that accumulate the elastic strain in the upper-plates of convergent zones are defined here as primary seismogenic structures. Several datasets of 1) modern upper-plate convergent strain, 2) historical earthquakes, 3) modern upper-plate vertical displacements, and 4) recent inter-plate events of Episodic Tremor and Slip (ETS) are compared to establish the extent of the primary seismogenic structure in the Cascadia convergent zone. The across-margin extents of 1) significant convergent strain, 2) margin-parallel bands of vertical displacement, 3) historical seismicity and 4) ETS events, representing inter-plate coupling and shear stress transfer to strain accumulation in the upper-plate, are used to map the width of the primary seismogenic structure. The across-margin width of the primary seismogenic structure in the central Cascadia margin ranges from 300 km in the south-central margin to 450 km in the north-central margin, as mapped landward from the buried trench. A broad source region of coseismic energy release in the Cascadia primary seismogenic structure (300 - 450 km width) could yield stronger shaking in interior metropolitan centers from a future major rupture of the mega-thrust than has been modeled from a narrow “locked” zone located offshore under the outer continental shelf. Despite low dip angle and associated wide inter-plate coupling, the Cascadia margin likely serves as an example of inter-plate shear stress transfer to elastic strain accumulation in the upper-plate of some other well-coupled convergent margins worldwide.