# large integers that are or might be the smallest of their kind

For the purpose of this feature, the arbitrary cutoff is ${10}^{7}$.

19099919 is the smallest prime to start a Cunningham chain^{} of length 8.

85864769 is the smallest prime to start a Cunningham chain of length 9.

545587687 is the smallest class 13+ prime in the Erdos-Selfridge classification of primes.

635318657 is the smallest number that can be expressed as a sum of two fourth powers in two different ways.

823766851 is the smallest prime with primitive root^{} 48.

906150257 is the smallest counterexample^{} to Pólya’s conjecture.

1023456789 is the smallest pandigital number in base 10.

1704961513 is the smallest class 14+ prime in the Erdős-Selfridge classification of primes.

10123457689 is the smallest pandigital prime in base 10.

26089808579 is the smallest prime to start a Cunningham chain of length 10.

665043081119 is the smallest prime to start a Cunningham chain of length 11.

554688278429 is the smallest prime to start a Cunningham chain of length 12.

${10}^{13}+1$ is, as of 2005, the smallest candidate for a counterexample to the Mertens conjecture^{} (though the smallest counterexample could turn out to be as large as $3.21\times {10}^{64}$).

4090932431513069 is the smallest prime to start a Cunningham chain of length 13.

95405042230542329 is the smallest prime to start a Cunningham chain of length 14.

810433818265726529159 is the smallest prime known to start a Cunningham chain of length 16, but there could be a smaller such prime.

439351292910452432574786963588089477522344721 is the smallest prime in Paul Hoffman’s erroneous version of Wilf’s primefree sequence^{} in which ${a}_{1}=3794765361567513$, ${a}_{2}=20615674205555510$ and ${a}_{n}={a}_{n-2}+{a}_{n-1}$ for $n>2$.

If an odd perfect number exists, it is at least ${10}^{300}+1$.

Title | large integers that are or might be the smallest of their kind |
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Canonical name | LargeIntegersThatAreOrMightBeTheSmallestOfTheirKind |

Date of creation | 2013-03-22 16:04:14 |

Last modified on | 2013-03-22 16:04:14 |

Owner | Mravinci (12996) |

Last modified by | Mravinci (12996) |

Numerical id | 15 |

Author | Mravinci (12996) |

Entry type | Feature |

Classification | msc 00A08 |

Related topic | SmallIntegersThatAreOrMightBeTheLargestOfTheirKind |