I have googled the question, but I do not believe the answers given by google to be accurate. All the answers point to a time period of around 4000 years which would bring us back to only 4000BC. However according to Wikipedia Adam was 930 years old when he died, Seth was 912, Enos was 905, Kenan was 910, Mahalalel was 895. Therefore we still have around 71 generations left to go and we are already beyond the 4000BC period.
~4ky is probably correct, although various dates have been given, some (according to Wikipedia, which I wouldn't trust as an unbiased source) reaching as far back as ~20ky. Most reputable estimates "top out" at ~6ky, and there are secondary evidences that place a maximum possible age of Earth at ~10ky or less. While precise opinions may vary, a Creation date of ~4000 B.C. to perhaps ~4500 B.C. is generally accepted. (Some may hold to a date of ~5500 B.C., which enjoyed wide consensus prior to the Masoretic Text.)
While it's true Adam lived to be quite old by modern standards, your "back of the envelope" calculation ignores that age at death is very, very different from age of first procreation. Seth, for instance, is attested as being born when Adam is 130. Others earlier in Jesus' lineage are born when their parents are roughly 70-200 years old. (Shem, born to a 502yo Noah, is a notable outlier.) Thus, even a pessimistic estimation based solely on number of generations gives a number of around ~9ky.
However, the Flood reduced the world population to eight humans (and even fewer of many animal kinds). The resulting genetic bottleneck had a severe impact on life expectancy, with lifespans rapidly falling off immediately after the flood before stabilizing again at around 70-100 years, which continues through today. Thus, a couple generations after Noah, we see that the average number of years between each generation in Jesus' lineage drops to around 30 (again with some notable exceptions, such as Abraham). Unsurprisingly, this value also persists to the present day.
Since only about 10-12 generations "waited so long" before producing the children in Jesus' lineage, they contribute about 1500 years, which is the time between Adam and the Flood. The remaining 60 generations, going solely by average time between generations, only give us another 1800 years; we're 700 years short! Of course, this difference is made up by the outliers, which can add hundreds of years each.
This article provides additional details of one particular dating attempt that should help explain where the date comes from.
Various factors (some explained in the previously cited article) affect these date calculations, and subtle interpretations such as what exactly a phrase like "in the fourth year of..." means can add up to a few dozen to perhaps a hundred years in different calculations. Larger discrepancies typically result from disagreements between the Septuagint and other textual sources on the ages of various patriarchs when they begat the sons in Jesus' lineage.
The several much greater numbers mentioned here are poorly substantiated, with the 20ky figure in particular having, as best I can determine, no information available online to back it up. Crawford's (~12ky) supporting material appears to deny the Genesis account and is thus automatically suspect. Another estimate (unclear whether it should be attributed to Camping or McOwen) gives 11ky based on what appear to be highly inflated generational ages; I would consider this estimate highly specious, though perhaps valid if looked at as a "worst case estimate" (that is, a maximum value that can still be Biblically justified, albeit by assuming that the stated generational ages are all unreliable).