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Was Fermat's Last Theorem known for infinitely many primes before Wiles?

Before Andrew Wiles's 1997 proof of Fermat's Last Theorem, in 1985, Étienne Fouvry proved that the first case of the equation holds for infinitely many primes $p$. Is there any infinite class of primes for which FLT could be known to hold, first case or otherwise, before Wiles's proof?