[raoulduke]

Correct. There can be no obvious link. Particularly in that Old Kingdom /r/ would reflect a Semitic /'/, if memory serves. So /pr/ would be the equivalent of /p'/ which would mean "mouth."

I likely compounded your confusion by referring to the grapheme as pr; whereas it is in fact Gardiner's O4, the monosyllabic /h/ (http://msheflin.blogspot.com/search/label/Early%20Alphabet - take the chart beyond /b/ with a grain of salt; I haven't updated it in years). This isn't my theory... this is basically the only consensus view on Proto-Sinaitic. Please stop wading into a crazy complex and insular, highly esoteric academic subject and then getting mad at me when you misunderstand my comments and attempt to construct a new orthodoxy around them...

The only connection between pr and b(y)t is semantic. Once you move from pure ideograms to logograms or abjads that wholly breaks down.

[posterboy]

I don't want to start a circular argument talking past each other. Wiktionary has for pr: "(Old Egyptian) IPA /paːruw/[1]". That's just one reconstruction but Its source is 20 years old so it could be outdated for all I know. Given your comments, I just see the glottal stop as another datapoint. Whether that also means "mouth" or not doesn't lead to confusion.

[1]: Hoch, James (1997) Middle Egyptian Grammar, Mississauga: Benben Publications, ISBN 0920168124, page 15