The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005042 Primes formed by the initial digits of the decimal expansion of Pi.
(Formerly M3129)
3, 31, 314159, 31415926535897932384626433832795028841 (list; graph; refs; listen; history; text; internal format)



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.

A naive probabilistic argument suggests that the sequence is infinite. [Michael Kleber, Jun 23 2004]


M. Gardner, personal communication.

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


Table of n, a(n) for n=1..4.

M. Gardner, Letter to N. J. A. Sloane, Nov 16 1979.

Ed T. Prothro, How I Found the Next Pi Prime

Eric Weisstein's World of Mathematics, Pi-Prime

Index entries for sequences related to "constant primes"

Index entries for sequences related to the number Pi


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


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:


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

nn=1000; With[{pidigs=RealDigits[Pi, 10, nn][[1]]}, Select[Table[FromDigits[ Take[pidigs, n]], {n, nn}], PrimeQ]] (* Harvey P. Dale, Sep 26 2012 *)


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


See A060421 for further terms.

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

Sequence in context: A118913 A297480 A282973 * A317482 A136582 A173649

Adjacent sequences:  A005039 A005040 A005041 * A005043 A005044 A005045




N. J. A. Sloane.



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 13:00 EST 2021. Contains 349429 sequences. (Running on oeis4.)