Prime is the opposite of Bad. Bad is related to Reputation. 
Teacher is etymologically related to Teach. Teacher is related to Test. Test can be Successful. Successful is a synonym of Lucky. 
Prime <--Antonym--> Bad <--RelatedTo--> Reputation 
Teach <--EtymologicallyRelatedTo-- Teacher <--RelatedTo--> Test --HasProperty--> Successful <--Synonym--> Lucky 