Has a near earth object in heliocentric orbit ever been bright enough to be visible to the unaided eye?
The Near-Earth close approches website shows close approaches to the Earth by near-Earth objects (NEOs). The table showing all close encounters indicates the absolute magnitude. 

The data can be exported to a CSV file to estimate the apparent magnitude for each object, using the following equation.

$$
m = H + 5 \log_{10} \bigg( \frac{d_{BS}d_{BO}}{d_0^2} \bigg) - q(\alpha)
$$
where $H$ is the absolute magnitude, $m$ is the apparent magnitude, d_{*} are the distances between the objects and $a(\alpha)$ is the reflected light. $q(\alpha)$ is a number between 0 and 1.

I only want to know what happens when the object is closest to the Earth, so I use the approximation that the distance from the Sun to the NEO is 1AU. 

$q(\alpha)$ is complicated to compute, so I just compute $m$ using $q=0$ and $q=1$. This leads to 

min value $ = H + 5 \log (d_{BO}) - 1 &lt; m &lt; H + 5 \log (d_{BO}) = $ max value

with $d_{BO}$ the distance between the Earth and the NEO expressed in astronomical units (AU). 

The server is unhappy when I try to get the entire database, so I limited my export to the objects that come reasonably close to Earth (d&lt;0.05 AU), with no time limit.

Among these 24588 objects, 4 have a maximal magnitude less than 6, and 16 have a minimal magnitude less than 6. So between 1900 and 2200, no more than 16 NEOs are visible by the naked eye.

In particular, 99942 Apophis (2004 MN4) has an apparent magnitude between 1.7 and 2.7 based on these estimates. Its close approach date is April 13 2029. 



But this doesn't say anything on NEOs from before 1900 or after 2200.