Editing Repunit (section)

==History==
Although they were not then known by that name, repunits in base-10 were studied by many mathematicians during the nineteenth century in an effort to work out and predict the cyclic patterns of [[repeating decimal]]s.<ref name="Dickson1999">{{Harvnb|Dickson|Cresse|1999|pp=164–167}}</ref>

It was found very early on that for any prime ''p'' greater than 5, the [[Repeating decimal|period]] of the decimal expansion of 1/''p'' is equal to the length of the smallest repunit number that is divisible by ''p''. Tables of the period of reciprocal of primes up to 60,000 had been published by 1860 and permitted the [[integer factorization|factorization]] by such mathematicians as Reuschle of all repunits up to ''R<sub>16</sub>'' and many larger ones. By 1880, even ''R<sub>17</sub>'' to ''R<sub>36</sub>'' had been factored<ref name="Dickson1999" /> and it is curious that, though [[Édouard Lucas]] showed no prime below three million had period [[19 (number)|nineteen]], there was no attempt to test any repunit for primality until early in the twentieth century. The American mathematician Oscar Hoppe proved ''R<sub>19</sub>'' to be prime in 1916,<ref>{{Harvnb|Francis|1988|pp=240–246}}</ref> and Lehmer and Kraitchik independently found ''R<sub>23</sub>'' to be prime in 1929.

Further advances in the study of repunits did not occur until the 1960s, when computers allowed many new factors of repunits to be found and the gaps in earlier tables of prime periods corrected. ''R<sub>317</sub>'' was found to be a [[probable prime]] circa 1966 and was proved prime eleven years later, when ''R<sub>1031</sub>'' was shown to be the only further possible prime repunit with fewer than ten thousand digits. It was proven prime in 1986, but searches for further prime repunits in the following decade consistently failed. However, there was a major side-development in the field of generalized repunits, which produced a large number of new primes and probable primes.

Since 1999, four further probably prime repunits have been found, but it is unlikely that any of them will be proven prime in the foreseeable future because of their huge size.

The [[Cunningham project]] endeavours to document the integer factorizations of (among other numbers) the repunits to base 2, 3, 5, 6, 7, 10, 11, and 12.