Talk:194 (number)

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 * http://transit.metrokc.gov/tops/bus/schedules/s194_0_.html
 * In 194 (number) on 2011-05-25 03:24:40, Socket Error: 'getaddrinfo failed'
 * In 194 (number) on 2011-06-04 17:23:13, Socket Error: 'getaddrinfo failed'

--JeffGBot (talk) 17:23, 4 June 2011 (UTC)

Not interesting enough to be mentioned in the article, but the only group of order 2194 - 1 is cyclic
Because 2194 - 1 = 3×971×1553×11447×31817×1100876018364883721×13842607235828485645766393 does not have a prime factor being congruent to 1 modulo another. I can't find any even number > 194 that has this property. If m is an even number such that every group of order 2m - 1 is cyclic, then 2m - 1 cannot have any prime factor congruent to 1 modulo 3; in particular, if p is an odd prime factor of m, then 22p - 1 = (2p - 1)(2p + 1) cannot have any prime factor congruent to 1 modulo 3. I could not find such a p other than 11, 23 and 97. 129.104.241.214 (talk) 00:12, 3 March 2024 (UTC)