Yes he did. Peter. Matthew 16:18.
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Oy vey.
No He didn’t. There is NO evidence those present construed His words to mean Peter was the Rock or had any special powers over and beyond the others. Not even Peter declared it (and he would if it were so). The best clues we have are Luke 22:24 and Matthew 18:1 and Mark 9:33-35 in repeated arguments about which of them “should be accounted the greatest”.