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A047658 Numbers n such that the initial n 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)



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


Table of n, a(n) for n=1..6.

C. K. Caldwell, Prime Curios: 14159...07021 (547-digits)


5 gives 14159 (prime); 12 gives 141592653589 (prime) and so on.


nn=1000; d=RealDigits[Pi-3, 10, nn][[1]]; Select[Range[nn], PrimeQ[FromDigits[Take[d, #]]] &]


(PARI) is(n)=isprime((Pi-3)*10^n\1) \\ Charles R Greathouse IV, Aug 28 2015


Cf. A000796 (Pi), A060421, A064118.

Sequence in context: A323565 A195538 A330218 * A290804 A353365 A146542

Adjacent sequences: A047655 A047656 A047657 * A047659 A047660 A047661




Carlos Rivera



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Last modified November 27 14:41 EST 2022. Contains 358405 sequences. (Running on oeis4.)