Taking a long time for oil primer to dry
24 hours is normal

The problem is, people who have only painted with latex paint have funny expectations about drying.  

Painting, and then sanding, in the same workday, is out of the question. 8 hours of dry isn't going to cut it for any alkyd, if the next step is to sand or switch from prime to topcoat. 

If it's taking more than 8 hours to get tack-free, or if it's taking longer than 24 hours to be sandable, you may be dealing with adverse conditions such as low temperature or poor air circulation.  You need to change the air periodically because it will saturate with the paint solvents, and that slows drying. (just like high humidity slows drying of water).  If your conditions are good, the next step is to talk to your paint supplier, because some paints are extra slow - they may have quick-dry additives available, to bring them into a "24 hours to sand" expectation.

By the way, "curing" is a red herring. For 1-part paints, curing takes months or even  years.  If it won't sand, it's not even dry.

Use primer for priming

In my experience, alkyd primers dry much faster than alkyd topcoats, which is why I'm surprised you're having a problem with primer. If you're actually painting a topcoat, and relying on some advertising claim that the paint is its own primer, yeah, that's a lie. That's always a lie. You'll never see a pro painter doing that. 

At the risk of stating the obvious, read the instructions

I think that's actually a law: it can do environmental damage, so you must use the product consistent with its instructions or labeling. A careful read of the paint-can fine print is essential, and if the fine print says "See instruction booklet" (as my 2-part paints do, as there isn't enough room on the label for critical warnings and also instructions), then you need to do that.  Not reading the instructions is the surest way to have mis-set expectations and a failed application. 

Also note that it is likely the instructions will call out certain "re-coat windows" which you have to hit. This is because of the (superior) nature of alkyd paints.   You generally have two recoat windows: between X and Y hours (when the paint is dry enough to be stable yet soft enough to chemically bond to the next coat); and beyond Z hours (when chemically bonding is no longer possible, but the paint is nice and hard so it can be scuff-sanded so the next coat can mechanically bond).  Adverse conditions can warp those numbers; conditions for slow drying extend them, etc. 

Chemical bonding has superior performance to mechanical bonding. If you've ever seen paint layers separate, that is someone relying on a mechanical bond and failing to do proper surface prep by scuff-sanding and cleaning.