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A047658 Numbers k such that the initial k digits in decimal portion of Pi form a prime number. 10
5, 12, 281, 547, 6205, 16350 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Conjecture: this sequence is finite. - Carlos Rivera
Rivera's conjecture that this sequence is finite conflicts with heuristics; the next entry is almost certainly 6205, since floor((Pi-3)*10^6205) is (very) probably prime, though its proof may take decades. - David Broadhurst, Nov 08 2000
Floor((Pi-3)*10^6205) is a strong pseudoprime to all (1229) prime bases a < 10000 (the test took 45 minutes). - Joerg Arndt, Jan 16 2011
Terms for n>=5 are only probable primes. - Dmitry Kamenetsky, Aug 03 2015
Floor((Pi-3)*10^16350) is a probable prime, checked with 25 iterations of the Miller-Rabin test. - Dmitry Kamenetsky, Aug 05 2015
The next term is greater than 65400. - Dmitry Kamenetsky, Aug 09 2015
LINKS
EXAMPLE
5 gives 14159 (prime); 12 gives 141592653589 (prime) and so on.
MATHEMATICA
nn=1000; d=RealDigits[Pi-3, 10, nn][[1]]; Select[Range[nn], PrimeQ[FromDigits[Take[d, #]]] &]
PROG
(PARI) is(n)=isprime((Pi-3)*10^n\1) \\ Charles R Greathouse IV, Aug 28 2015
(Python)
from sympy import S, isprime
pi_digits = str(S.Pi.n(10**5))[2:-1]
def afind():
kint = 0
for k in range(len(pi_digits)):
kint = 10*kint + int(pi_digits[k])
if isprime(kint):
print(k+1, end=", ")
afind() # Michael S. Branicky, Jan 29 2023
CROSSREFS
Cf. A000796 (Pi), A060421, A064118.
Sequence in context: A323565 A195538 A330218 * A290804 A353365 A146542
KEYWORD
hard,nice,nonn,base,more
AUTHOR
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)