In Harry Potter and the Half-Blood Prince during the potions class Slughorn claimed that the prize of Felix Felicis was won only once before by a student.

I should point out, however, only once did a student manage to brew a potion of sufficient quality to claim this prize. Nevertheless, good luck to you all.

Who could that student be? What could they have done with the potion?

Almost certainly Snape

The Harry Potter wikia has an article for the student aptly named Unidentified Potions student. In it, it identifies Tom Riddle, Snape and Lilly as possible candidates.

• This student may have been a member of the Slug Club, as Professor Slughorn accepts talented students.




• It is possible that this student may have been Tom Riddle, but is more likely it may have been Severus Snape or Lily Evans who were both known to have had an aptitude for Potions.

However, we know that Harry was using the recipes from a book that Snape had written in notes and helpful hints and his own recipes in so it would seem most likely Snape was the prior student. This seems all the more true when we look into how good Snape was at potions.

Apparently the movie and book represent alternate realities, because this never happened in the book. However, if it would have happened in the book, we can venture a guess that Snape would have been the previous student.

Later in the book (Chapter Fifteen), Slughorn discusses Harry's Potions ability with other teachers, and he mentions the amazing Draught of Living Death that Harry concocted (my emphasis):

"But I don't think I've ever known such a natural at Potions!" said Slughorn, regarding Harry with a fond, if bloodshot, eye. "Instinctive, you know — like his mother! I've only ever taught a few with this kind of ability, I can tell you that, Sybill — why even Severus —" And to Harry's horror, Slughorn threw out an arm and seemed to scoop Snape out of thin air toward them. "Stop skulking and come and join us, Severus!" hiccuped Slughorn happily. "I was just talking about Harry's exceptional potion-making! Some credit must go to you, of course, you taught him for five years!"

Trapped, with Slughorn's arm around his shoulders, Snape looked down his hooked nose at Harry, his black eyes narrowed. "Funny, I never had the impression that I managed to teach Potter anything at all."

"Well, then, it's natural ability!" shouted Slughorn. "You should have seen what he gave me, first lesson, Draught of Living Death — never had a student produce finer on a first attempt, I don't think even you, Severus —"

In the first paragraph he implies that Snape was the best at Potions prior to Harry. In the last paragraph he implies that Snape's attempt at the Draught of Living Death was the next best after Harry's.

If there had truly only been one previous student to brew one sufficiently worthy of the prize it would then stand to reason that this student was Snape.

Of course, this is not ironclad evidence as it is possible that Slughorn used Snape as the example because Snape was there, even if there may have been one or two students that were better than him.

It was Tom Riddle. Yes Snape's handbook provides a fool proof way of brewing the potion, but the way the 6th HP movie presents a specific scene makes me rethink that it was Tom. The pineapple sweets. It was the scene where Harry is recalling one of Slughorn's memories in the Pensieve. If we assume Tom has taken liquid luck just prior to the meeting, the scene makes so much sense. The scene begins with Tom asking Slughorn if a certain professor will retire, Tom is probably testing the effects of liquid luck and wanting to get confidential information from Slughorn. Slughorn replies, "well I couldn't tell you even if I knew could I?" Which indicates that providing the effects of liquid luck, to make all of your endeavours succeed as long as possible, Slughorn did in fact not know this information, otherwise he would have shared it. The next line is the killer of this theory really. Professor Slughorn says, "By the way, thank you for the pineapple you are quite right it is my favourite...but how did you know?" to which Tom mysteriously replies "...Intuition." In fact, Tom's use of liquid luck allowed him to correctly identify and purchase Slughorne's favourite sweets, probably in attempts to ease him up to share information about the hocruxes. As we learn later in the movie, he in fact reveals the truth about hocruxes to Tom, thanks to tom's use of liquid luck. What makes this theory especially disturbing is that Slughorn massively regrets this memory, probably because he thinks he helped Tom Riddle achieve power and spread evil and misery in the world when he told him about the hocruxes, not to mention killing one of his favourite students and Harry's mother, Lily. But Slughorn doesn't know that his defences were simply down due to the liquid luck he had awarded his student for properly brewing the potion known as Living Dead. Or perhaps in the back of his mind, he does know liquid luck was used against him and regrets having given it to Tom. Evidence for this could be the way he fantasises about reacting angrily to Tom's request about the hocruxes. Probably how the true encounter would have gone about if not for Tom's use of liquid luck.