A296444 Numbers k such that 2*10^(2k) + 2*10^k + 1 are prime.
0, 2, 3, 6, 10, 276, 746, 1090, 1485, 6186, 8571, 15594
Offset: 1
Examples
5, 20201, 2002001, 2000002000001, and 200000000020000000001 are prime, while 221=13*17, 200020001=569*351529, and 20000200001=17*29*1129*35933.
Programs
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Mathematica
ParallelMap[ If[ PrimeQ[2*10^(2 #) + 2*10^# + 1], #, Nothing] &, Range@ 6500] (* Robert G. Wilson v, Dec 13 2017 *)
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PARI
isok(k) = isprime(2*10^(2*k)+2*10^k+1); \\ Michel Marcus, Dec 13 2017
Extensions
a(6)-a(7) from Michel Marcus, Dec 13 2017
a(8)-a(10) from Robert G. Wilson v, Dec 13 2017
a(1) = 0 inserted by Seiichi Manyama, Aug 15 2019
a(11) from Michael S. Branicky, Apr 16 2023
a(12) from Michael S. Branicky, Apr 30 2025
Comments