innumerable but many

An indefinite number, usu. more than ten and less than one hundred; a lot. Often used hyperbolically, and usually expressing the notion of more than the usual number or more than I would like.

Umpteen is a term for an unspecified but large number, used in a humorous fashion or to imply that it is not worth the effort to pin down the actual figure. Generally, it refers to the number of times something has happened, rather than to a number of objects. Since many people use the word in a facetious manner, it is not considered a scientifically or mathetically useful term.