ARE YOU A CHIEF STUDENT?
David Friedman, in They Loved the Torah p. 61 comments about Peter (Shim'on):
I see Shim'on as Yeshua's Torah-observant....talmid hakham...a Hebrew technical term meaning the leading student (of a rabbi). Every famous rabbi who daily taught the same students had a talmid hakham, his chief student. This is the student who figured most prominently in narratives about his rabbi. In first-century Judaism, the chief student was trusted by his rabbi to learn and pass on the rabbi's teachings. The Talmud provides an example of this type of relationship...
Friedman then quotes the Talmud, Avot 2:10-12, for examples as to how rabbis would praise their disciples based upon their personal qualities:
Rabban Yochanan ben Zakkai had five disciples and these are they: Eliezer ben Hyrcanus, Joshua ben Chananiah, Yosi the Priest, Shimon ben Natanel, and Elazar ben Arach. He used to say their praise:
Eliezer ben Hyrcanus is a plastered cistern which does not lose a drop;
Joshua ben Chananiah -- happy is she that gave birth to him;
Yosi the Priest is a saintly man;
Shimon ben Natanel is fearful of sin;
Elazar ben Arach is an ever-flowing spring.
He used to say: If all the sages of Israel were in one scale of the balance and Eliezer ben Hyrcanus in the other, he would outweigh them all.