The phrase "appreciable number" means a significant or noticeable amount or quantity. It refers to a number that is large enough to be worthy of attention or consideration. Full definition
«The real takeaway from our study is that this is happening in appreciable numbers and it's happening to trainees, so people who are either students or postdocs, people who are really vulnerable,» she added. (scientificamerican.com)
But still, eight years after Bitcoin launched, Satoshi Nakamoto remains the only creator to have built a blockchain that an appreciable number of ordinary people actually want to use. (techcrunch.com)
But the politicians who dole out money aren't particularly interested in funding mathematicians because that isn't going to win any appreciable number of votes - but wasteful spending will lose votes, as will cuts to welfare, nutrition programs, education, etc.. (politics.stackexchange.com)