Andy, I have a disconnect here.
Raw eggs are OK for weeks but once they are boiled they are only good for one week?
Cooking, of course, is a way of preserving food, it denatures the proteins and makes them less susceptible to bacterial action. Also the boiling, it would seem to me, would kill most of the bacteria there.
And if a refrigerated raw egg is OK to use for 5 weeks or so, why does cooking it reduce its shelf life?
It seems to me that if one can make thousand year old eggs by placing raw eggs in the ground merely surrounded by some tea, salt, ashes, and lime for 100 days, and then eat them, a hard boiled egg, refrigerated, should last more than one week.
Not telling anyone to keep boiled eggs longer than that, but something does not seem to add up.
Sorry, it is the middle of the night and I am feeling a bit fussy.