The answer to this depends on the viewing distance.

The usual rule of 300 PPI works well for close-up viewing, but even that isn't a hard-and-fast rule. What's more important is Pixels-Per-Degree (PPD), which is more representative of our eye's ability to resolve detail, and is dependent on a specific/typical viewing distance.

Apple's Retina displays (picking theirs just because there's abundant info, there are other similar concepts around) are designed based on PPD rather than PPI. Basically, PPD refers to the number of pixels spanned by a 1-degree arc from your eye, when viewing the screen/image.

The basic formulas to convert between PPI and PPD, for a given viewing distance d are:

PPD = d * PPI * 2 * tan(pi/360)     ≈ d * PPI * 0.01745
PPI = PPD / (d * 2 * tan(pi/360))   ≈ PPD / (d * 0.01745)
  d = PPD / (PPI * 2 * tan(pi/360)) ≈ PPD / (PPI * 0.01745)

Note: Assumes tan() is working in radians.

Now Apple's threshold for 'Retina' PPD is 53, though their displays are mostly 70–85, though the iPhones with highest PPI of 326 but lowest viewing distance are about 57 PPD. This roughly matches the recommendations for small photos of ~300 PPI, which are also often viewed at around 25cm (10") distance.

Others suggest up to 100 PPD (especially for people with better than 20/20 vision), so there's a large range for what is acceptable. You may need to pick your own PPD threshold here, probably somewhere between 50 and 100.

So what does this mean?

For a large print viewed at a distance, you don't necessarily need to keep the 300 PPI rule. Viewing from 3 metres away (~118") you could get away with about 30–50 PPI for 53–100 PPD (try looking at some large street advertising up close and see how huge the 'pixels' are printed).

Incidentally (and slightly off-topic), since viewing distance often increases roughly linearly with image size (for certain applications), you can potentially do away with these PPI and PPD concepts entirely for certain applications.

Typically*, images are viewed from a distance that makes viewing them in their entirety comfortable. So if the image is 10 metres (~400") wide, you won't be standing 25cm (10") from it, you'll be standing perhaps 12 metres (~470") away (giving a viewing angle of 45º, roughly the view of a 45mm lens on full-frame camera). This would allow a printed resolution of around 6.5–12 PPI! This will scale directly with the printed size, so there's simply a minimum resolution required for this given viewing angle of around 2400–4700 pixels across. If it's only going to be viewed as a whole, with a 45-degree viewing angle across the image, then the larger you print it, the further you stand back—image resolution is all that matters. And in that sense, something like an 8MP camera (2400x3200) or 15MP (3200x4800) is always enough for such purposes, regardless of print size.

*Not all images are viewed this way, hence why there's still a push for higher resolution cameras, and higher resolution images, so I'm certainly not saying high resolution doesn't matter.

And this is especially true for huge panoramas, where the whole point is to view the fine details in a huge image. Viewers will be looking closely at small areas, and so it comes back to the simple viewing distance calculations.

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Now down to printing your 15k-pixel-wide panorama...

If you print it ~2.4m (8') wide, you'll get 156 PPI, which would give a minimum viewing distance range of about 0.5 to 1 metres (19–37") for 53–100 PPD.

You then have to decide whether this is acceptable, given the intended location of the print, the room it's in, access to the image, the likely audience, etc.