2 She ran, therefore, and cometh to Simon Peter, and to the other disciple whom Jesus loved, and saith to them: They have taken away the Lord out of the sepulchre, and we know not where they have laid him. 3 Peter therefore went out, and that other disciple, and they came to the sepulchre. 4 And they both ran together, and that other disciple did outrun Peter, and came first to the sepulchre. 5 And when he stooped down, he saw the linen cloths lying; but yet he went not in. 6 Then cometh Simon Peter, following him, and went into the sepulchre, and saw the linen cloths lying,
Why else would St. John refrain from entering if it was not for the primacy of St. Peter?