Wieferich primes and Barker sequences, II
Peter Borwein and Michael J. Mossinghoff

22 integers u < 10^13 that were eliminated as a possible order of a
circulant Hadamard matrix, using Turyn's self-conjugacy criterion.  Each
value is shown with the values of r and s used to show that u is not
admissible under Turyn's test (Theorem 2 in the present article).

           u              Factor(u)             r             Factor(r)                    s                         Factor(s)
      1806259         [7,13,23,863]        258037           [13,23,863]            125865961                   [13,13,863,863]
  21457753699     [23,83,821,13691]     258527153        [23,821,13691]      126344591376721             [821,821,13691,13691]
  25360477365   [3,5,31,2903,18787]        449965           [5,31,2903]     5948931087345842         [2,2903,2903,18787,18787]
  38250778333     [41,83,821,13691]     460852751        [41,821,13691]      126344591376721             [821,821,13691,13691]
  56506380421      [431,2393,54787]     131105291          [2393,54787]    17188597328194681           [2393,2393,54787,54787]
 132313052319  [3,7,1657,1667,2281]          1667                [1667] 79395663555421457042 [2,1657,1657,1667,1667,2281,2281]
 144914295397   [23,1657,1667,2281]          1667                [1667] 79395663555421457042 [2,1657,1657,1667,1667,2281,2281]
 169519141263    [3,431,2393,54787]     131105291          [2393,54787]    17188597328194681           [2393,2393,54787,54787]
 174268586145  [3,5,31,18043,20771]        643901            [31,20771]   280906834241898818       [2,18043,18043,20771,20771]
 177523341555 [3,5,7,31,2903,18787]        449965           [5,31,2903]   291497623279946258     [2,7,7,2903,2903,18787,18787]
 220521753865  [5,7,1657,1667,2281]   44104350773    [7,1657,1667,2281]       14285504666689             [1657,1657,2281,2281]
 245724240021 [3,13,1657,1667,2281]   81908080007   [13,1657,1667,2281]       14285504666689             [1657,1657,2281,2281]
 282531902105    [5,431,2393,54787]     131105291          [2393,54787]    17188597328194681           [2393,2393,54787,54787]
 384337913879   [61,1657,1667,2281]  384337913879   [61,1657,1667,2281]       14285504666689             [1657,1657,2281,2281]
 409540400035 [5,13,1657,1667,2281]   81908080007   [13,1657,1667,2281]       28571009333378           [2,1657,1657,2281,2281]
 508557423789  [3,3,431,2393,54787]     131105291          [2393,54787]    17188597328194681           [2393,2393,54787,54787]
 573356560049 [7,13,1657,1667,2281]  573356560049 [7,13,1657,1667,2281]       14285504666689             [1657,1657,2281,2281]
 621570184631   [11,431,2393,54787]     131105291          [2393,54787]    34377194656389362         [2,2393,2393,54787,54787]
 734582945473   [13,431,2393,54787]     131105291          [2393,54787]    34377194656389362         [2,2393,2393,54787,54787]
 825381421609  [131,1657,1667,2281]  825381421609  [131,1657,1667,2281]       14285504666689             [1657,1657,2281,2281]
1153013741637 [3,61,1657,1667,2281]  384337913879   [61,1657,1667,2281]       28571009333378           [2,1657,1657,2281,2281]
2690365397153 [7,61,1657,1667,2281] 2690365397153 [7,61,1657,1667,2281]       28571009333378           [2,1657,1657,2281,2281]