Talk:194 (number)

Dead link

During several automated bot runs the following external link was found to be unavailable. Please check if the link is in fact down and fix or remove it in that case!

• 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 2^m - 1 is cyclic, then 2^m - 1 cannot have any prime factor congruent to 1 modulo 3; in particular, if p is an odd prime factor of m, then 2^2p - 1 = (2^p - 1)(2^p + 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)