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Are there any three distinct digits a,b,ca, b, ca,b,c such that all six permutations abc‾,acb‾,bac‾,bca‾,cab‾,cba‾\overline{abc}, \overline{acb}, \overline{bac}, \overline{bca}, \overline{cab}, \overline{cba}abc,acb,bac,bca,cab,cba are prime numbers?
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