Regular Expressions have nothing to do with the question asked because there is no US standard for distinguishing "fax numbers" from other POTS line dedicated to data, nor from voice lines.

Consider your home telephone line(s):

• If you have a fax (hardware or software) attached, is that a fax number?
• If that line is also used for oral communications, is it a fax line?
• Is it still a fax line if you installed it for use with a fax machine and have kept it as an extra voice line since you turned off the machine?

JavaFan and others have made this point in various manners.

The question is moot or needs refinement.

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