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

3, 31, 314159, 31415926535897932384626433832795028841

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base

Comments

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

References

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

Links

• 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

Crossrefs

See A060421 for further terms.

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

Programs

Maple

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:

Mathematica

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

Formula

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