A060421 Numbers n such that the first n digits of the decimal expansion of Pi form a prime.

1, 2, 6, 38, 16208, 47577, 78073, 613373

Offset

1,2

Comments

The Brown link states that in 2001 Ed T. Prothro reported discovering that 16208 gives a probable prime and that Prothro verified that all values for 500 through 16207 digits of Pi are composites. - Rick L. Shepherd, Sep 10 2002

The corresponding primes are in A005042. - Alexander R. Povolotsky, Dec 17 2007

Links

Table of n, a(n) for n=1..8.

K. S. Brown, Primes in the Decimal Expansion of Pi [Broken link?]

K. S. Brown, Primes in the Decimal Expansion of Pi [Cached copy]

Prime Curios, 314159

Prime Curios, 31415...36307 (16208-digits)

Eric Weisstein's World of Mathematics, Constant Primes

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Eric Weisstein's World of Mathematics, Pi Digits

Eric Weisstein's World of Mathematics, Pi-Prime

Example

3 is prime, so a(1) = 1; 31 is prime, so a(2) = 2; 314159 is prime, so a(3) = 6; ...

Mathematica

Do[If[PrimeQ[FromDigits[RealDigits[N[Pi, n + 10], 10, n][[1]]]], Print[n]], {n, 1, 9016} ]

Crossrefs

Cf. A000796 (Pi), A005042, A007523, A047658.

Primes in other constants: A064118 (e), A065815 (gamma), A064119 (phi), A118328 (Catalan's constant), A115377 (sqrt(2)), A119344 (sqrt(3)), A228226 (log 2), A228240 (log 10), A119334 (zeta(3)), A122422 (Soldner's constant), A118420 (Glaisher-Kinkelin constant), A174974 (Golomb-Dickman constant), A118327 (Khinchin's constant).

Sequence in context: A353535 A072191 A118324 * A054970 A211348 A295912

Adjacent sequences: A060418 A060419 A060420 * A060422 A060423 A060424

Keyword

hard,nonn,base

Author

Michel ten Voorde, Apr 05 2001

Extensions

a(6) = 47577 from Eric W. Weisstein, Apr 01 2006

a(7) = 78073 from Eric W. Weisstein, Jul 13 2006

a(8) = 613373 from Adrian Bondrescu, May 29 2016

Status

approved