A mid tone, not a primary
Every other colour on this site is fully saturated: one or more channels at 255, the rest at zero. Purple here is #800080, which is red and blue at roughly half power. That difference is the point. A panel driving a channel at half power has to be accurate about it, and cheap panels are not, so a flat mid tone field exposes dithering patterns, temporal noise and banding that a saturated primary hides completely.
Look for a fine grain crawling across the field, which is temporal dithering, and for a slight difference in tone between the top and the bottom of the screen, which is a gamma uniformity problem.
Purple lines and purple casts
If you came here because a purple line is running down your screen, this page will show you whether it is on the panel or in the signal. Open the purple screen full screen and look at the line. If it is still there, and it is still there on the white and black screens too, it is a panel or connector fault. If it disappears on some colours, the fault is more likely in the graphics output or the cable.
A general purple or magenta cast across everything usually means the green channel is weak, not that anything is purple. The green screen is the faster test for that.
The friendliest colour to stare at
Of the ten screens here, a mid purple is the one most people can look at for a long stretch without discomfort. It is dark enough not to glare and coloured enough not to feel like a dead monitor, which makes it a reasonable choice for a standby screen, a photography backdrop, or a blank surface to think in front of.