A282973 Primes in A011546.
3, 31, 314159, 314159265359
Offset: 1
Examples
a(5) = A011546(1902) = 314159...066118631 is a prime with 1902 digits. a(6) = A011546(3971) = 314159...411010447. a(7) = A011546(5827) = 314159...690496521. a(8) = A011546(16208) = A005042(5) = 314159....943936307. For n<=17511, there are eight primes in sequence A011546(n). In addition, because of round(Pi*10^47576) = floor(Pi*10^47576), and A011546(47577)(=A005042(6)) is a prime. Thus, A011546(47577) will appear in here. A011546(613373)(=A005042(8)) as well. But A011546(78073)(=A005042(7)+1) is not prime.
Links
- Eric Weisstein's World of Mathematics, Pi-Prime
Programs
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Mathematica
Do[If[PrimeQ[Round[Pi*10^(n-1)]],Print[Round[Pi*10^(n-1)]]],{n,17511}] Select[Module[{nn=20,pid},pid=RealDigits[Pi,10,nn+2][[1]];Table[Floor[(FromDigits[ Take[ pid,n+1]])/10+1/2],{n,nn}]],PrimeQ] (* Harvey P. Dale, Jan 01 2023 *)