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A047658
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Numbers k such that the initial k digits in decimal portion of Pi form a prime number.
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10
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OFFSET
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1,1
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COMMENTS
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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
Floor((Pi-3)*10^16350) is a probable prime, checked with 25 iterations of the Miller-Rabin test. - Dmitry Kamenetsky, Aug 05 2015
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LINKS
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EXAMPLE
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5 gives 14159 (prime); 12 gives 141592653589 (prime) and so on.
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MATHEMATICA
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nn=1000; d=RealDigits[Pi-3, 10, nn][[1]]; Select[Range[nn], PrimeQ[FromDigits[Take[d, #]]] &]
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PROG
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(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=", ")
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CROSSREFS
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KEYWORD
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hard,nice,nonn,base,more
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AUTHOR
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STATUS
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approved
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