First off, I already noted that Jerusalem was a Great City in the 1st Century AD whose "suburbs" extended well beyond the city gates. At the time of Passover, it's population quadrupled from 250,000 to over one million residents and pilgrims within a "Sabbath's day journey" of the city (not within the city walls itself).
Now then -- Howzabout we look to Infallible Scripture for some evidence as to the Population of Jerusalem and Israel in the 1st Century AD? In the first place, since the 2 Samuel informs us that the able-bodied men of Israel numbered some 1.3 million in David's day (II Samuel 24:9), we can estimate a total population of at least 4-5 million in the Israel of King David. Thus, an estimate of 2-3 million in the general area of 1st-Century Syro-Palestine is not unreasonable, nor is an estimate of 250,000 in the City of of Seven Mountains (Jerusalem) and its suburbs.
Furthermore, Acts 21:20 informs us that there were "many myriads" of believing Messianic Jews in the area of Jerusalem alone (Acts 21:17,20; "they" being contrasted to the "Jews which are among the Gentiles" in Acts 21:21) -- literally, many tens of thousands (a plural "myriad" giving us at least 20,000, but "many myriads" giving us more like 30-50,000).
If there were at least 20-50,000 believing Messianic Jews in the area of Jerusalem and its suburbs by the time of Acts 21, just what do you suppose was the total population? Certainly vastly higher than your paltry estimate of 10,000; again, an estimate of 250,000 is reasonable, and here the testimony of Josephus and Tacitus enjoys support from the direct testimony of Scripture itself.
best, OP
Where's the Seven Mountains OP? I CAN'T SEE THEM.
Can you point to any other Roman "great city" so far from the seacoast or a river (and thus ready access to grain and fuel)?
At the time of Passover, it's population quadrupled from 250,000 to over one million residents and pilgrims within a "Sabbath's day journey" of the city (not within the city walls itself).
Define "suburbs". Provide a citation for 250,000 as the ordinary population.
Now then -- Howzabout we look to Infallible Scripture for some evidence as to the Population of Jerusalem and Israel in the 1st Century AD? In the first place, since the 2 Samuel informs us that the able-bodied men of Israel numbered some 1.3 million in David's day (II Samuel 24:9), we can estimate a total population of at least 4-5 million in the Israel of King David. Thus, an estimate of 2-3 million in the general area of 1st-Century Syro-Palestine is not unreasonable, nor is an estimate of 250,000 in the City of of Seven Mountains (Jerusalem) and its suburbs.
Numeric citations in Scripture are quite problematic at times, as the differences between the Septuagint and the Masoretic show, scribal error is easy to introduce. I'd accept it as infallible scripture if you could prove to me it is in the autograph.
2-3 million seems inflated. I'd possibly believe around 1 million, with an urbanized population of perhaps 10%.
http://www.tulane.edu/~august/H303/handouts/Population.htm
Cites 6.5 million for Syria, Palestine, and northern Mesopotamia (Edessa/Nisbis).
Other interesting citations:
http://intarch.ac.uk/antiquity/storey.html
"What was the population of imperial Rome? City blocks in Pompeii and Ostia are sufficiently well explored that a fair estimate of population density can now be arrived at. That peoples the city of ancient Rome with roughly 450,000 inhabitants, within the known population and density range of pre-industrial and modern urban centres."
http://philtar.ucsm.ac.uk/encyclopedia/judaism/ancisr.html
You have to remember, the biggest difficulty with populations is feeding them and getting them water. If you want a large population in Jerusalem, how do you get the food there overland, and where is the water soruce and ancient aquaducts?