The primer 3' ends when annealed to the target DNA are closer to one another than the 5' ends are. Theoretically, a geometric amplification of a fragment whose ends are defined by the 5' ends of the primers should occur, while the longer template sequence is amplified at most arithmetically. The availability of thermostable polymerases and the design of thermal cycler machines made PCR widely accessible. Synthesis times can be manipulated to guarantee just the synthesis of shorter DNAs. PCR is extremely sensitive.
Contamination is a constant worry.
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