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MATHEMATICA
| Select[Prime[Range[10!]], IntegerDigits[#]==Reverse[IntegerDigits[#]] && IntegerDigits[#, 2]==Reverse[IntegerDigits[#, 2]]&] (*From Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), Dec 30 2010*)
p = Sort[Reap[Do[d=IntegerDigits[n]; p1=FromDigits[Join[Most[d], Reverse[d]]]; p2=FromDigits[Join[d, Reverse[d]]]; If[IntegerDigits[p1, 2] == Reverse[IntegerDigits[p1, 2]], Sow[p1]]; If[IntegerDigits[p2, 2] == Reverse[IntegerDigits[p2, 2]], Sow[p2]], {n, 0, 9999999}]][[2, 1]]]; Select[p, PrimeQ]
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