If the substrate is primary, can we rule out SN1 and E1 entirely?

No. You should assume that `E1` and `S_N1` may still happen to some extent, because they usually still do.

Many factors contribute to that occurring; for primary alkyl halides in particular, they may include:

• nucleophile strength
• nucleophile steric hindrance and bulkiness
• solvent steric hindrance and bulkiness
• solvent interactions (nonpolar, polar protic, polar aprotic)
• reaction temperature
• etc.

Let us take some examples that I'm pulling from one of my 2013 worksheets:

(The given product ratios were on the worksheet as-is.)

You can tell that the substrate each time is a primary alkyl halide, but clearly there are exceptions that allow for elimination to occur, even at normal temperatures.

In the first one, the phase-transferable (organic/aqueous solubility) tetrabutylammonium chloride (t-BuNCl) nucleophile is extremely strong and is not hindered by the organic polar aprotic solvent, promoting substitution. This has no `E1` or `E2`, but has an unknown mixture of `S_N1` and `S_N2`.

In the second one, the nucleophile is pretty strong but not extremely so, and interacting with an organic polar protic solvent via H-bonding decreases the nucleophilicity, decreasing the amount of substitution by a bit. This has `S_N2`, some `E2`, and little `S_N1` and `E1`, but still some.

In the third one, the steric hindrance of the nucleophile promotes elimination, particularly `E2` and `E1`, but also allows for some `S_N1`. Likely no `S_N2` because the bulkiness on the nucleophile prevents it from finding the substrate quickly.