Voter turnout in U.S. primary elections is very low. On average, only 20% of eligible nationwide voters participate in primaries. This raises questions about whether primary electorates distort representation in state legislatures and Congress. States frequently experiment with different rules about who can participate in primaries, such as adopting nonpartisan primaries to increase participation. This study uses individual-level panel data from state voter files nationwide to investigate whether nonpartisan and open primaries are associated with higher voter turnout in congressional primaries across multiple elections. While previous research using aggregate data or single-state case studies finds modest effects, the results of this study show that individuals living in nonpartisan primary states are 12 percentage points more likely to vote in the 2022 midterm elections compared to people living in closed or semi-closed primary states, controlling for other factors including electoral competition. The results further suggest that partisans and independents are more likely to vote in nonpartisan primary elections; independents uniquely benefit from the nonpartisan primary. Electoral competition in Senate and gubernatorial races is found to significantly boost turnout in primaries of all types.