cp's OEIS Frontend

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

%I A060421 #47 Aug 02 2025 12:15:19
%S A060421 1,2,6,38,16208,47577,78073,613373
%N A060421 Numbers k such that the first k digits of the decimal expansion of Pi form a prime.
%C A060421 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
%C A060421 The corresponding primes are in A005042. - _Alexander R. Povolotsky_, Dec 17 2007
%H A060421 K. S. Brown, <a href="http://www.sixfingeredman.net/ref/mathpages-notes/kmath184/kmath184.htm">Primes in the Decimal Expansion of Pi</a> [Broken link?]
%H A060421 K. S. Brown, <a href="/A060421/a060421.htm">Primes in the Decimal Expansion of Pi</a> [Cached copy]
%H A060421 Prime Curios, <a href="https://t5k.org/curios/page.php?short=314159">314159</a>
%H A060421 Prime Curios, <a href="https://t5k.org/curios/page.php?number_id=1435">31415...36307 (16208-digits)</a>
%H A060421 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_19">Mystery of pi</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 19, 473-497.
%H A060421 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConstantPrimes.html">Constant Primes</a>
%H A060421 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%H A060421 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PiDigits.html">Pi Digits</a>
%H A060421 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Pi-Prime.html">Pi-Prime</a>
%e A060421 3 is prime, so a(1) = 1; 31 is prime, so a(2) = 2; 314159 is prime, so a(3) = 6; ...
%t A060421 Do[If[PrimeQ[FromDigits[RealDigits[N[Pi, n + 10], 10, n][[1]]]], Print[n]], {n, 1, 9016} ]
%Y A060421 Cf. A000796 (Pi), A005042, A007523, A047658.
%Y A060421 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).
%Y A060421 In other bases: A065987 (binary), A065989 (ternary), A065991 (quaternary), A065990 (quinary), A065993 (senary).
%K A060421 hard,nonn,base,more
%O A060421 1,2
%A A060421 _Michel ten Voorde_, Apr 05 2001
%E A060421 a(6) = 47577 from _Eric W. Weisstein_, Apr 01 2006
%E A060421 a(7) = 78073 from _Eric W. Weisstein_, Jul 13 2006
%E A060421 a(8) = 613373 from _Adrian Bondrescu_, May 29 2016