WASHINGTON – DNA testing all but confirmed Thomas Jefferson slept with his slave Sally Hemings. Now it’s rewriting another lurid chapter in presidential history, this one from the Roaring ’20s. Genetic analysis has proved that President Warren G. Harding fathered a child with long-rumored mistress Nan Britton, according to AncestryDNA, a DNA-testing division of Ancestry.com. Britton set off a Jazz Age sex scandal when she went public with her tale of forbidden love in the White House, boldly publishing her story in a 1927 best-selling memoir, “The President’s Daughter.” But historians long questioned her claims, and Harding defenders vilified her as a liar for nearly 90 years. Based on DNA from Britton’s grandson and descendants of Harding, the results are 99.9 percent certain, Ancestry said.