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# eliminated Sierpiński number candidates

Most numbers $k$ are very easy to eliminate as Sierpiński number candidates, as it is very easy to come up with sequences of primes of the form $k2^{n}+1$. For example, for $k=1$ it is enough to mention the Fermat primes. For some of the seventeen Sierpiński number candidates when the Seventeen or Bust project began, only a single Proth prime, and it is often quite large. Eight candidates remain to be eliminated. The primes listed below were discovered by the Seventeen or Bust project, with the latest being for 19249, discovered by user Konstantin Agafonov of team TSC! Russia.

$k$ | Exponent $n$ which gives prime | Prime in base 10 scientific notation |
---|---|---|

4847 | 3321063 | $1.844857508381060\times 10^{{999743}}$ |

5359 | 5054502 | $2.781168752802502\times 10^{{1521560}}$ |

10223 | Still a candidate | N/A |

19249 | 13018586 | $1.484360328715661\times 10^{{3918989}}$ |

21181 | Still a candidate | N/A |

22699 | Still a candidate | N/A |

24737 | Still a candidate | N/A |

27653 | 9167433 | $5.727724120920733\times 10^{{2759676}}$ |

28433 | 7830457 | $7.772839072447348\times 10^{{2357206}}$ |

44131 | Still a candidate | N/A |

46157 | Still a candidate | N/A |

54767 | Still a candidate | N/A |

55459 | 995972 | $1.234767571821004\times 10^{{299822}}$ |

65567 | 1013803 | $8.499227304459893\times 10^{{305189}}$ |

67607 | Still a candidate | N/A |

69109 | 1157446 | $6.366429016367452\times 10^{{348430}}$ |

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## Mathematics Subject Classification

11A51*no label found*

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