In order for a PCR reaction to work, the primers must be within reasonable distances of each other. Consider the reaction shown in the following figure:

As shown at the bottom the figure, the two primers anneal to the products of the first cycle of DNA synthesis.

The DNA polymerase must synthesize a product long enough such that it contains the site for annealing to the other primer. Otherwise, PCR can't continue.

Theoretically, DNA synthesis should continue until the DNA polymerase reaches the end of the DNA template molecule. However, this is not the case experimentally. Eventually, the DNA polymerase will literally "fall off" of the DNA template.

How soon the polymerase falls off of the template depends on the template itself. If the DNA is very pure and clean, the polymerase should be able to stay on the template for at least 4000 to 6000 base pairs, allowing the synthesis of a PCR product which is 400 to 6000 base pairs in length. However, if the DNA is not very clean and pure, the impurities will interfere with the DNA polymerase, causing it to fall off prematurely.

In the case of the onion DNA preparations done in the Waksman Onion Project (where we are unable to use chemicals which can make the DNA very pure), the DNA polymerase will probably not be able to synthesize PCR products longer than 1000 base pairs. Therefore, in order for PCR to be successful, the PCR primers must anneal to sites within 1000 base pairs of each other.