

A005042


Primes formed by the initial digits of the decimal expansion of Pi.
(Formerly M3129)


29




OFFSET

1,1


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

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, PiPrime
Index entries for sequences related to "constant primes"
Index entries for sequences related to the number Pi


FORMULA

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


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 *)


PROG

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


CROSSREFS

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


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane.


STATUS

approved



