In the 20th century, Venn diagrams were further developed. David Wilson Henderson showed, in 1963, that the existence of an "n"-Venn diagram with "n"-fold rotational symmetry implied that "n" was a prime number. He also showed that such symmetric Venn diagrams exist when "n" is five or seven. In 2002, Peter Hamburger found symmetric Venn diagrams for "n" = 11 and in 2003, Griggs, Killian, and Savage showed that symmetric Venn diagrams exist for all other primes. These combined results show that rotationally symmetric Venn diagrams exist, if and only if "n" is a prime number.