The estimate is probably going to depend on the source, but it's generally at least an order of magnitude more than that.
Back in 2002, John Moore, an anthropologist at the University of Florida, calculated that a starship could leave Earth with 150 passengers on a 2000-year pilgrimage to another solar system, and upon arrival, the descendants of the original crew could colonize a new world there—as long as everyone was careful not to inbreed along the way. [...]
A starting population of 40,000 people maintains 100 percent of its variation, while the 10,000-person scenario stays relatively stable too. So, Smith concludes that a number between 10,000 and 40,000 is a pretty safe bet when it comes to preserving genetic variation.
For the general concept see minimum viable population.