Of a telephone number, not in the directory; unlisted(adjective)
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Use "ex-directory" in a sentence
"They heard nothing more until a worrying set of messages was left by somebody called "Lou" on both their mobiles and their ex-directory landline, stating they had to call and quote a reference number in order to receive some very important personal news."
"That was on my first day in here, and to this day he has yet to explain how he got my home telephone number (I'm ex-directory)."
"He said they had told him his mobile phone number, ex-directory landline number and address had been found in records made by Mulcaire that were recovered from the investigator's office in south London."