cp's OEIS Frontend

A005042 Primes formed by the initial digits of the decimal expansion of Pi.

%I A005042 M3129 #44 Feb 16 2025 08:32:28
%S A005042 3,31,314159,31415926535897932384626433832795028841
%N A005042 Primes formed by the initial digits of the decimal expansion of Pi.
%C A005042 The next term consists of the first 16208 digits of Pi and is too large to show here (see A060421). Ed T. Prothro found this probable prime in 2001.
%C A005042 A naive probabilistic argument suggests that the sequence is infinite. - _Michael Kleber_, Jun 23 2004
%D A005042 M. Gardner, personal communication.
%D A005042 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005042 M. Gardner, <a href="/A005042/a005042.pdf">Letter to N. J. A. Sloane,</a> Nov 16 1979.
%H A005042 Ed T. Prothro, <a href="https://web.archive.org/web/20050320060313/http://ourworld.compuserve.com/homepages/prothro/how.htm">How I Found the Next Pi Prime</a>.
%H A005042 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Pi-Prime.html">Pi-Prime</a>.
%H A005042 <a href="/index/Co#constant_primes">Index entries for sequences related to "constant primes"</a>
%H A005042 <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>
%F A005042 a(n) = floor(10^(A060421(n)-1)*A000796), where A000796 is the constant Pi = 3.14159... . - _M. F. Hasler_, Sep 02 2013
%p A005042 Digits := 130; n0 := evalf(Pi); for i from 1 to 120 do t1 := trunc(10^i*n0); if isprime(t1) then print(t1); fi; od:
%t A005042 a = {}; Do[k = Floor[Pi 10^n]; If[PrimeQ[k], AppendTo[a, k]], {n, 0, 160}]; a (* _Artur Jasinski_, Mar 26 2008 *)
%t A005042 nn=1000;With[{pidigs=RealDigits[Pi,10,nn][[1]]},Select[Table[FromDigits[ Take[pidigs,n]],{n,nn}],PrimeQ]] (* _Harvey P. Dale_, Sep 26 2012 *)
%o A005042 (PARI) c=Pi;for(k=0,precision(c),isprime(c\.1^k) & print1(c\.1^k,",")) \\ - _M. F. Hasler_, Sep 01 2013
%Y A005042 See A060421 for further terms.
%Y A005042 Cf. A198018, A198019, A195834, A047777, A053013, A064467.
%K A005042 nonn,base
%O A005042 1,1
%A A005042 _N. J. A. Sloane_