One Friday morning at the end of September, a troupe of about 18 city, county, and state officials gathered on the seventh floor of Atlantic City’s stubby modernist city hall for an all-day workshop. The job at hand: Brainstorm ideas for the city’s application for a grant sponsored by Bloomberg Philanthropies. The nonprofit’s 2017 Mayor’s Challenge offers cities the opportunity to win a $5 million grand prize (or, for four runner’s up, a $1 million consolation prize). All Atlantic City has to do to score the jackpot was come up with a brilliant pitch to beat out 554 other Mayor’s Challenge applicants. This was the 300th such workshop Bloomberg Philanthropies has held in recent months, and the prospect of the prize drew the mayor, his chief of staff, the chief of police, the city planning director, the business administrator, the city grant-writer, five officials from the New Jersey Economic Development Authority, the executive director of the county economic alliance, and an assortment of officials from other institutions who do business in the city.