Singer only made 500. That's why they go for six figures.
And Singers are not the rarest 1911s. That title would go to the North American Arms company, a Canadian company, in Quebec, who contracted the Ross Rifle Co. to produce the guns. ( That was a mistake. The Ross Rifle company was turning out Mk III rifles at the time that were failing miserably in the trenches. ) There were only about 100 produced. The NAA guns had some unusual features, like an uncheckered hammer spur, which was longer than usual. That must have been fun, because the short grip safety was present. Hello severe hammer bite !!!
The pistols were contracted for by the U.S. government, but production problems caused the entire project to crash and burn.
Despite their rarity they do not bring the top dollar like the Singer's do. I am too computer stupid to know haw to post a link. Just google " North American Arms Co 1911 " to see pics.