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

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

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.

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 LargeIntegersThatAreOrMightBeTheSmallestOfTheirKind 2013-03-22 16:04:14 2013-03-22 16:04:14 Mravinci (12996) Mravinci (12996) 15 Mravinci (12996) Feature msc 00A08 SmallIntegersThatAreOrMightBeTheLargestOfTheirKind