I'm not sure what "pure white" versus "dun white" is. Could you explain and provide photos of the differences? As far as I know, the silver gene is not necessary to produce a nice white bird. It is a pattern gene, not a color gene per se.
"The genes dominant white and recessive white cause the entire bird to be white. The silver gene only effects certain ares of the birds body- in males it effects the pyle zone and in females it effects the hackles and to some extent specific areas of the body. Silver and gold are at the same locus, dominant white is at another locus and recessive white is at a different locus than the other genes. the silver gene would help create the primary color pattern. The primary color pattern is produced by the silver and or gold genes in combination with the E locus gene. Silver is a pattern gene and does not create a white bird on it's own." Quote from poultry geneticist.
"The genes dominant white and recessive white cause the entire bird to be white. The silver gene only effects certain ares of the birds body- in males it effects the pyle zone and in females it effects the hackles and to some extent specific areas of the body. Silver and gold are at the same locus, dominant white is at another locus and recessive white is at a different locus than the other genes. the silver gene would help create the primary color pattern. The primary color pattern is produced by the silver and or gold genes in combination with the E locus gene. Silver is a pattern gene and does not create a white bird on it's own." Quote from poultry geneticist.