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The population of Twin Peaks was originally only supposed to be 5,120. However, there was a backlash against rural-themed shows at the time, so ABC requested that the sign read 51,201. In a "Visitor's Guide to Twin Peaks" tie-in book authorized by creators David Lynch and Mark Frost, a note tells readers that the population was indeed 5,120, but that the sign had a "typo."
The character of Madeleine Ferguson (Laura Palmer's lookalike cousin, played by the same actress) was created because David Lynch was so impressed by Sheryl Lee that he wanted to have her on the series full-time.