%I M3129 #43 Oct 26 2023 23:15:57

%S 3,31,314159,31415926535897932384626433832795028841

%N Primes formed by the initial digits of the decimal expansion of Pi.

%C 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 A naive probabilistic argument suggests that the sequence is infinite. - _Michael Kleber_, Jun 23 2004

%D M. Gardner, personal communication.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H M. Gardner, <a href="/A005042/a005042.pdf">Letter to N. J. A. Sloane,</a> Nov 16 1979.

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Pi-Prime.html">Pi-Prime</a>.

%H <a href="/index/Co#constant_primes">Index entries for sequences related to "constant primes"</a>

%H <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>

%F a(n) = floor(10^(A060421(n)-1)*A000796), where A000796 is the constant Pi = 3.14159... . - _M. F. Hasler_, Sep 02 2013

%p 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 a = {}; Do[k = Floor[Pi 10^n]; If[PrimeQ[k], AppendTo[a, k]], {n, 0, 160}]; a (* _Artur Jasinski_, Mar 26 2008 *)

%t 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 (PARI) c=Pi;for(k=0,precision(c),isprime(c\.1^k) & print1(c\.1^k,",")) \\ - _M. F. Hasler_, Sep 01 2013

%Y See A060421 for further terms.

%Y Cf. A198018, A198019, A195834, A047777, A053013, A064467.

%K nonn,base

%O 1,1

%A _N. J. A. Sloane_