Green’s Dictionary of Slang

1. (US) an important person, also attrib.

1942		Davis & Wolsey Call House Madam 20: A lot of big numbers who’d made the steep grade and landed in the top brackets.
1957		A. James ‘Body on a White Carpet’ in Best of Manhunt (2019) [ebook] He was feeling like one of the big number boys with this girl at his side. It was about time he was getting up in the world.
1960		(con. 1940s) G. Morrill Dark Sea Running 216: I’m just an ordinary little dope [...] I loved the big number who ditched me.
1960, 1975		Wentworth & Flexner DAS.

2. (US prison) one who poses as more important in the outside world than is the truth.

1950

Goldin et al. DAUL 27/2: Big number. (P) (Slightly derisive) A convict who affects airs on the basis of a white-collar job, possession of sums of money sent steadily by friends or relatives, the knack of being a prison success, etc.