Not a correct question, would not be easy to get good answers.
But just to give something for you to think: Do all bacteria have antibiotic resistance gene(s)? And are they resistant to a particular or all antibiotics?
Bacteria can share genes with each other by horizontal gene transfer. This can occur between bacteria of the same species and between different species using several different mechanisms like conjugation, transduction or transformation when the conditions provided are suitable. Gene transfer causes genetic variation in bacteria and this becomes dangerous when it comes to spread of antibiotic resistance genes. Whether the transferred genes including antibiotic resistance gene will be integrated into the DNA of the recipient bacterium is also not certain. If the incoming DNA is beneficial to the recipient bacterium, then it is likely to be maintained by the recipient like for instance the antibiotic resistance gene in order to survive. But if the foreign DNA is harmful to the recipient bacterium, then it can be degraded by the recipient. But these ways are not 100% efficient. It all depends on the environmental conditions in which the bacteria prevail.
So, I don’t think the antibiotic resistance gene is same for all bacteria.
1. There's many different antibiotics, and they often have a limited spectrum of organisms they effect.
Examples:
Penicillin causes bacterial death by inhibiting cell wall synthesis. This made it useful for Gram positive bacteria, which have their cell wall on the outside, but it wasn't very good against some Gram negative bacteria, partly because their cell wall is hidden behind a membrane.
Rifampicin is an antibiotic with a totally different mechanism of action, it works by inhibiting RNA synthesis instead.
2. Resistance can arise by multiple different mechanisms.
Example:
You have a strain resistant to the antibiotic streptomycin, which binds to a ribosomal subunit and prevents bacteria from synthesizing proteins. This strain could have a ribosomal mutation which prevents streptomycin from binding. Or it could have a type of enzyme that chemically alters streptomycin and prevents it from binding to its target site.
3. Even within specific mechanisms there's variations.
Example:
Beta-lactamases are enzymes that inactivate penicillin-like antibiotics. There are many of these in circulation right now, and there's no single ancestor to all beta-lactamase genes. Many of them have mutated extensively in transit to the point where it's not even clear where they originated exactly.
Point being, "antibiotic resistance gene" is a very broad category, and you might not even be able to find universal primers for one type of resistance gene.