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If primers weren't present in PCR at what temperature would DNA re-anneal? I am wondering how primers manage to bind on DNA strands before DNA manages to anneal back together.

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To answer your second question, one of the main reasons primers anneal before your target re-anneals to itself is not because it binds stronger, but because you add primers in large molar excess to their targets. The primers will find your template faster than your template will find another matching template, and once the primer is annealed the template cant bind onto another template even if that reaction is more energetically favorable. This molar excess is a requirement for the exponential amplification in PCR, and when you start to lose the excess primer concentration you lose exponential increase due to your targets re-annealing (and you get the production of unwanted PCR artifacts like chimeras). As for the temperature, it depends on your template, but I guess it has to be somewhere between the primer annealing temp and the temp of your melting step.

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