SPARTANBURG, S.C. — Republicans’ turnout streak continued, with GOP voters shattering their South Carolina primary record Saturday night.

With almost all precincts reporting, more than 737,000 votes had been counted. That was more than 20 percent higher than 2012, when about 603,000 voted.

It follows record GOP turnout in Iowa’s caucuses and New Hampshire’s primary earlier this month.

By contrast, Democrats’ turnout has tumbled from its 2008 records in all three contests, including Saturday’s caucuses in Nevada. About 80,000 voters took part in the caucuses, with was 33 percent less than 2008’s level.

Republicans hold their caucuses Tuesday in Nevada, while Democrats shift to South Carolina next weekend.

Taken together, some 1.2 million people have voted in Republican primaries and caucuses so far. That’s up 24.1 percent over the level in 2012, which is the last time the GOP had a contested nomination.

Democrats, meanwhile, have seen about 504,000 people vote in their three contests in Iowa, New Hampshire and South Carolina down 22.4 percent from their last contested primary in 2008.

Analysts have cautioned against reading too much into turnout figures at this point, saying the bigger test of enthusiasm and momentum will come next week in the Super Tuesday slate of contests.

Of the total votes cast so far on the GOP side, Mr. Trump has won 31.8 percent of all of them. The other major candidates in the race Sen. Ted Cruz holds a slight advantage over Sen. Marco Rubio, with 20.6 percent of the total votes to Mr. Rubio’s 19.7 percent. Ohio Gov. John Kasich trails with 8.6 percent, and retired neurosurgeon Ben Carson has garnered 6.4 percent of the total votes case.

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