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 16208-digit probable prime has been proved prime; see the Prime Curios reference below. - RJ Baillie, May 18 2026
The corresponding primes are in A005042. - Alexander R. Povolotsky, Dec 17 2007
LINKS
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)
Shyam Sunder Gupta, Mystery of pi, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 19, 473-497.
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
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).
KEYWORD
hard,nonn,base,more
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
