All The , 2, -continued fractions of the first, 200, primes By Shalosh B. Ekhad The square-roots of the following primes do not seem to have an umtimately \ periodic,, 2, -continued fraction judging by the first, 2000, terms [193, 211, 263, 389, 409, 421, 431, 509, 521, 593, 599, 607, 613, 617, 631, 643 , 661, 751, 809, 811, 823, 877, 887, 907, 919, 937, 947, 953, 967, 1021, 1033, 1039, 1049, 1051, 1069, 1097, 1109, 1171, 1187, 1201] Among those that do, the largest period is the square-root of, 487, whose period is, 136 Here are all the successful ones 2, : , [[1], [4, 2]] 3, : , [[1], [2]] 5, : , [[2], [8, 4]] 7, : , [[2], [3, 20, 3, 4]] 11, : , [[3], [6]] 13, : , [[3], [3, 6]] 17, : , [[4], [16, 8]] 19, : , [[4], [5, 3, 4, 34, 4, 3, 5, 8]] 23, : , [[4], [2, 3, 2, 8]] 29, : , [[5], [5, 10]] 31, : , [[5], [3, 3, 2, 4, 2, 3, 3, 10]] 37, : , [[6], [24, 12]] 41, : , [[6], [4, 2, 24, 2, 4, 12]] 43, : , [[6], [3, 3, 4, 2, 34, 13, 34, 2, 4, 3, 3, 12]] 47, : , [[6], [2, 5, 2, 12]] 53, : , [[7], [7, 14]] 59, : , [[7], [2, 2, 14]] 61, : , [[7], [2, 4, 7, 4, 2, 14]] 67, : , [[8], [10, 2, 3, 2, 3, 6, 2, 2, 2, 64, 2, 2, 2, 6, 3, 2, 3, 2, 10, 16]] 71, : , [[8], [4, 2, 2, 7, 2, 2, 4, 16]] 73, : , [[8], [3, 2, 2, 22, 34, 22, 2, 2, 3, 16]] 79, : , [[8], [2, 7, 2, 16]] 83, : , [[9], [18]] 89, : , [[9], [4, 3, 6, 2, 36, 2, 6, 3, 4, 18]] 97, : , [[9], [2, 5, 3, 8, 12, 2, 8, 2, 12, 8, 3, 5, 2, 18]] 101, : , [[10], [40, 20]] 103, : , [[10], [13, 4, 3, 9, 3, 4, 13, 20]] 107, : , [[10], [5, 2, 4, 5, 2, 19, 2, 5, 4, 2, 5, 20]] 109, : , [[10], [4, 3, 2, 2, 9, 2, 2, 3, 4, 20]] 113, : , [[10], [3, 11, 3, 2, 41, 2, 3, 11, 3, 20]] 127, : , [[11], [7, 4, 2, 2, 3, 44, 3, 2, 2, 4, 7, 22]] 131, : , [[11], [4, 4, 22]] 137, : , [[11], [2, 2, 5, 11, 5, 2, 2, 22]] 139, : , [[11], [2, 3, 2, 3, 15, 10, 5, 2, 2, 6, 3, 3, 12, 94, 12, 3, 3, 6, 2, 2, 5, 10, 15, 3, 2, 3, 2, 22]] 149, : , [[12], [9, 2, 2, 13, 7, 3, 780, 3, 7, 13, 2, 2, 9, 24]] 151, : , [[12], [6, 2, 15, 3, 2, 4, 12, 2, 2, 10, 8, 5, 3, 2, 2, 3, 2, 23, 2, 3, 2, 2, 3, 5, 8, 10, 2, 2, 12, 4, 2, 3, 15, 2, 6, 24]] 157, : , [[12], [3, 2, 3, 4, 2, 2, 2, 8, 5, 5, 2, 7, 3, 2, 11, 2, 3, 7, 2, 5, 5, 8, 2, 2, 2, 4, 3, 2, 3, 24]] 163, : , [[12], [2, 3, 6, 2, 3, 2, 3, 4, 5, 2, 16, 11, 8, 2, 2, 5, 2, 2, 8, 11, 16, 2, 5, 4, 3, 2, 3, 2, 6, 3, 2, 24]] 167, : , [[12], [2, 11, 2, 24]] 173, : , [[13], [13, 26]] 179, : , [[13], [5, 7, 7, 2, 25, 2, 7, 7, 5, 26]] 181, : , [[13], [4, 4, 2, 8, 13, 8, 2, 4, 4, 26]] 191, : , [[13], [2, 4, 3, 3, 3, 220, 3, 3, 3, 4, 2, 26]] 193, : , FAIL 197, : , [[14], [56, 28]] 199, : , [[14], [18, 2, 2, 2, 4, 5, 9, 56, 9, 5, 4, 2, 2, 2, 18, 28]] 211, : , FAIL 223, : , [[14], [2, 13, 2, 28]] 227, : , [[15], [30]] 229, : , [[15], [15, 30]] 233, : , [[15], [7, 3, 3, 2, 3, 60, 3, 2, 3, 3, 7, 30]] 239, : , [[15], [4, 5, 2, 2, 8, 15, 8, 2, 2, 5, 4, 30]] 241, : , [[15], [3, 2, 4, 4, 2, 3, 30]] 251, : , [[15], [2, 5, 5, 4, 2, 2, 7, 9, 4, 24, 2, 6, 2, 24, 4, 9, 7, 2, 2, 4, 5, 5, 2, 30] ] 257, : , [[16], [64, 32]] 263, : , FAIL 269, : , [[16], [4, 2, 64, 2, 4, 32]] 271, : , [[16], [4, 6, 21, 3, 16, 2, 10, 3, 2, 13, 2, 6, 2, 4, 5, 25, 2, 31, 2, 25, 5, 4, 2, 6, 2, 13, 2, 3, 10, 2, 16, 3, 21, 6, 4, 32]] 277, : , [[16], [3, 18, 5, 4, 3, 2, 2, 5, 29, 8, 5, 10, 2, 2, 3, 2, 65, 2, 3, 2, 2, 10, 5, 8, 29, 5, 2, 2, 3, 4, 5, 18, 3, 32]] 281, : , [[16], [2, 3, 9, 26, 3, 7, 8, 5, 16, 5, 8, 7, 3, 26, 9, 3, 2, 32]] 283, : , [ [16], [2, 4, 3, 14, 5, 4, 7, 2, 21, 3, 3, 21, 2, 7, 4, 5, 14, 3, 4, 2, 32]] 293, : , [[17], [17, 34]] 307, : , [[17], [3, 2, 5, 23, 140, 23, 5, 2, 3, 34]] 311, : , [[17], [3, 13, 4, 4, 2, 16, 2, 4, 4, 13, 3, 34]] 313, : , [[17], [2, 2, 8, 11, 3, 3, 3, 62, 5, 2, 6, 4, 2, 2, 3, 2, 2, 4, 6, 2, 5, 62, 3, 3, 3, 11, 8, 2, 2, 34]] 317, : , [[17], [2, 4, 17, 4, 2, 34]] 331, : , [[18], [10, 5, 2, 6, 4, 3, 3, 4, 6, 2, 5, 10, 36]] 337, : , [[18], [5, 3, 5, 4, 2, 14, 8, 83, 2, 2, 27, 2, 72, 4, 6, 2, 2, 334, 2, 59, 7, 2, 8, 8, 3, 8, 8, 2, 7, 59, 2, 334, 2, 2, 6, 4, 72, 2, 27, 2, 2, 83, 8, 14, 2, 4, 5, 3, 5, 36]] 347, : , [[18], [3, 10, 2, 4, 8, 2, 9, 2, 3, 148, 3, 2, 9, 2, 8, 4, 2, 10, 3, 36]] 349, : , [[18], [2, 2, 14, 7, 5, 2, 17, 2, 5, 7, 14, 2, 2, 36]] 353, : , [[18], [2, 3, 2, 2, 3, 8, 6, 3, 5, 2, 3, 2, 5, 3, 6, 8, 3, 2, 2, 3, 2, 36]] 359, : , [[18], [2, 17, 2, 36]] 367, : , [[19], [12, 2, 2, 3, 3, 4, 25, 19, 25, 4, 3, 3, 2, 2, 12, 38]] 373, : , [[19], [6, 5, 10, 3, 76, 3, 10, 5, 6, 38]] 379, : , [[19], [4, 7, 6, 2, 4, 6, 25, 3, 20, 17, 9, 3, 8, 7, 10, 2, 5, 3, 4, 5, 2, 3, 2, 6, 2, 154, 2, 6, 2, 3, 2, 5, 4, 3, 5, 2, 10, 7, 8, 3, 9, 17, 20, 3, 25, 6, 4, 2, 6, 7, 4, 38]] 383, : , [[19], [3, 3, 2, 18, 2, 3, 3, 38]] 389, : , FAIL 397, : , [[19], [2, 12, 6, 4, 19, 4, 6, 12, 2, 38]] 401, : , [[20], [80, 40]] 409, : , FAIL 419, : , [[20], [4, 7, 2, 2, 7, 4, 40]] 421, : , FAIL 431, : , FAIL 433, : , [[20], [2, 4, 8, 2, 5, 3, 2, 13, 19, 4, 3, 3, 9, 3, 2, 3, 3, 2, 20, 68, 10, 33, 3, 2, 7, 15, 2, 4, 6, 3, 3, 2, 2, 3, 2, 3, 2, 2, 3, 3, 6, 4, 2, 15, 7, 2, 3, 33, 10, 68, 20, 2, 3, 3, 2, 3, 9, 3, 3, 4, 19, 13, 2, 3, 5, 2, 8, 4, 2, 40]] 439, : , [[20], [2, 19, 2, 40]] 443, : , [[21], [42]] 449, : , [[21], [10, 3, 3, 33, 5, 2, 2, 10, 4, 2, 6, 2, 8, 2, 4, 5, 122, 2, 10, 2, 4, 135, 9, 2, 2, 41, 2, 2, 9, 135, 4, 2, 10, 2, 122, 5, 4, 2, 8, 2, 6, 2, 4, 10, 2, 2, 5, 33, 3, 3, 10, 42]] 457, : , [[21], [5, 6, 2, 2, 2, 2, 6, 5, 42]] 461, : , [[21], [4, 8, 21, 8, 4, 42]] 463, : , [[21], [3, 2, 6, 4, 2, 3, 6, 2, 23, 2, 2, 3, 10, 5, 10, 3, 2, 2, 23, 2, 6, 3, 2, 4, 6, 2, 3, 42]] 467, : , [[21], [3, 7, 9, 2, 9, 2, 9, 7, 3, 42]] 479, : , [[21], [2, 7, 2, 3, 4, 21, 4, 3, 2, 7, 2, 42]] 487, : , [[22], [29, 5, 7, 16, 2, 20, 4, 5, 5, 2, 2, 2, 201, 78, 4, 4, 2, 43, 6, 6, 2, 18, 2, 3, 49, 2, 14, 5, 5, 9, 6, 3, 7, 17, 7, 20, 13, 7, 2, 3, 3, 4, 2, 3, 3, 3, 2, 2, 2, 4, 3, 7, 2, 4, 3, 12, 2, 2, 2, 4, 7, 3, 6, 5, 2, 3, 3, 43, 3, 3, 2, 5, 6, 3, 7, 4, 2, 2, 2, 12, 3, 4, 2, 7, 3, 4, 2, 2, 2, 3, 3, 3, 2, 4, 3, 3, 2, 7, 13, 20, 7, 17, 7, 3, 6, 9, 5, 5, 14, 2, 49, 3, 2, 18, 2, 6, 6, 43, 2, 4, 4, 78, 201, 2, 2, 2, 5, 5, 4, 20, 2, 16, 7, 5, 29, 44]] 491, : , [[22], [12, 3, 8, 8, 3, 12, 44]] 499, : , [[22], [5, 2, 10, 5, 2, 43, 2, 5, 10, 2, 5, 44]] 503, : , [[22], [4, 2, 2, 21, 2, 2, 4, 44]] 509, : , FAIL 521, : , FAIL 523, : , [[22], [2, 6, 3, 19, 2, 2, 3, 3, 2, 3, 2, 2, 13, 4, 37, 42, 2, 181, 2, 42, 37, 4, 13, 2, 2, 3, 2, 3, 3, 2, 2, 19, 3, 6, 2, 44]] 541, : , [ [23], [7, 2, 2, 4, 4, 8, 2, 5, 2, 3, 92, 3, 2, 5, 2, 8, 4, 4, 2, 2, 7, 46]] 547, : , [[23], [5, 12, 2, 30, 7, 2, 2, 2, 2, 3, 5, 2, 10, 2, 5, 3, 2, 2, 2, 2, 7, 30, 2, 12, 5, 46]] 557, : , [[23], [3, 6, 23, 6, 3, 46]] 563, : , [[23], [2, 2, 2, 2, 46]] 569, : , [[23], [2, 5, 2, 5, 18, 2, 2, 2, 6, 3, 5, 5, 3, 6, 2, 2, 2, 18, 5, 2, 5, 2, 46]] 571, : , [[23], [2, 8, 3, 4, 4, 2, 7, 13, 5, 127, 36, 5, 47, 5, 36, 127, 5, 13, 7, 2, 4, 4, 3, 8, 2, 46]] 577, : , [[24], [96, 48]] 587, : , [[24], [8, 2, 3, 6, 11, 2, 4, 10, 2, 192, 2, 10, 4, 2, 11, 6, 3, 2, 8, 48]] 593, : , FAIL 599, : , FAIL 601, : , [[24], [3, 2, 7, 4, 2, 3, 5, 3, 2, 12, 6, 3, 4, 6, 3, 12, 4, 8, 43, 5, 2, 3, 7, 2, 23, 3, 12, 5, 173, 2, 16, 3, 13, 8, 9, 52, 24, 20, 62, 3, 62, 20, 24, 52, 9, 8, 13, 3, 16, 2, 173, 5, 12, 3, 23, 2, 7, 3, 2, 5, 43, 8, 4, 12, 3, 6, 4, 3, 6, 12, 2, 3, 5, 3, 2, 4, 7, 2, 3, 48]] 607, : , FAIL 613, : , FAIL 617, : , FAIL 619, : , [[24], [2, 7, 6, 5, 9, 3, 4, 8, 3, 7, 2, 5, 2, 3, 198, 3, 2, 5, 2, 7, 3, 8, 4, 3, 9, 5, 6, 7, 2, 48]] 631, : , FAIL 641, : , [[25], [6, 6, 2, 9, 7, 3, 4, 2, 15, 5, 8, 5, 4, 2, 2, 14, 101, 14, 2, 2, 4, 5, 8, 5, 15, 2, 4, 3, 7, 9, 2, 6, 6, 50]] 643, : , FAIL 647, : , [[25], [4, 3, 4, 2, 3, 3, 6, 6, 36, 2, 2, 14, 2, 49, 2, 14, 2, 2, 36, 6, 6, 3, 3, 2, 4, 3, 4, 50]] 653, : , [[25], [3, 3, 7, 6, 6, 28, 2, 7, 2, 11, 2, 7, 2, 28, 6, 6, 7, 3, 3, 50]] 659, : , [[25], [2, 2, 50]] 661, : , FAIL 673, : , [[25], [2, 16, 6, 5, 4, 3, 3, 2, 2, 2, 12, 8, 4, 25, 4, 8, 12, 2, 2, 2, 3, 3, 4, 5, 6, 16, 2, 50]] 677, : , [[26], [104, 52]] 683, : , [[26], [14, 2, 8, 3, 3, 2, 12, 7, 37, 2, 2, 2, 3, 12, 3, 2, 2, 2, 37, 7, 12, 2, 3, 3, 8, 2, 14, 52]] 691, : , [[26], [6, 2, 34, 10, 4, 5, 5, 4, 10, 34, 2, 6, 52]] 701, : , [[26], [4, 10, 20, 2, 104, 2, 20, 10, 4, 52]] 709, : , [[26], [3, 10, 3, 3, 8, 13, 2, 29, 3, 2, 105, 2, 3, 29, 2, 13, 8, 3, 3, 10, 3, 52] ] 719, : , [[26], [2, 4, 5, 8, 9, 3, 2, 9, 2, 25, 2, 9, 2, 3, 9, 8, 5, 4, 2, 52]] 727, : , [[26], [2, 25, 2, 52]] 733, : , [[27], [27, 54]] 739, : , [[27], [10, 2, 5, 15, 10, 8, 2, 6, 5, 3, 4, 2, 18, 3, 2, 11, 2, 2, 53, 2, 2, 11, 2, 3, 18, 2, 4, 3, 5, 6, 2, 8, 10, 15, 5, 2, 10, 54]] 743, : , [[27], [7, 2, 3, 108, 3, 2, 7, 54]] 751, : , FAIL 757, : , [[27], [3, 2, 8, 4, 2, 3, 4, 2, 2, 3, 2, 7, 27, 7, 2, 3, 2, 2, 4, 3, 2, 4, 8, 2, 3, 54]] 761, : , [[27], [3, 4, 2, 6, 27, 6, 2, 4, 3, 54]] 769, : , [[27], [2, 2, 2, 2, 3, 2, 8, 4, 5, 27, 5, 4, 8, 2, 3, 2, 2, 2, 2, 54]] 773, : , [[27], [2, 4, 27, 4, 2, 54]] 787, : , [[28], [37, 5, 4, 2, 3, 8, 2, 2, 2, 2, 4, 4, 3, 24, 5, 3, 6, 55, 2, 4, 22, 6, 13, 2, 4, 8, 2, 2, 2, 2, 3, 6, 5, 3, 8, 2, 3, 13, 3, 2, 8, 3, 5, 6, 3, 2, 2, 2, 2, 8, 4, 2, 13, 6, 22, 4, 2, 55, 6, 3, 5, 24, 3, 4, 4, 2, 2, 2, 2, 8, 3, 2, 4, 5, 37, 56]] 797, : , [[28], [8, 3, 27, 3, 8, 56]] 809, : , FAIL 811, : , FAIL 821, : , [[28], [3, 32, 22, 2, 6, 9, 2, 2, 17, 3, 24, 4, 10, 2, 8, 2, 1832, 2, 8, 2, 10, 4, 24, 3, 17, 2, 2, 9, 6, 2, 22, 32, 3, 56]] 823, : , FAIL 827, : , [ [28], [2, 3, 15, 2, 13, 4, 3, 3, 10, 14, 10, 3, 3, 4, 13, 2, 15, 3, 2, 56]] 829, : , [[28], [2, 3, 2, 4, 4, 3, 5, 11, 12, 3, 8, 2, 27, 2, 8, 3, 12, 11, 5, 3, 4, 4, 2, 3, 2, 56]] 839, : , [[28], [2, 27, 2, 56]] 853, : , [[29], [9, 2, 2, 5, 2, 4, 116, 4, 2, 5, 2, 2, 9, 58]] 857, : , [[29], [7, 7, 58]] 859, : , [[29], [6, 4, 11, 7, 3, 16, 2, 3, 14, 2, 6, 3, 3, 2, 4, 4, 2, 2, 17, 6, 14, 6, 17, 2, 2, 4, 4, 2, 3, 3, 6, 2, 14, 3, 2, 16, 3, 7, 11, 4, 6, 58]] 863, : , [[29], [5, 6, 3, 2, 7, 3, 10, 29, 10, 3, 7, 2, 3, 6, 5, 58]] 877, : , FAIL 881, : , [[29], [2, 2, 14, 11, 2, 2, 2, 3, 2, 4, 3, 6, 2, 5, 29, 5, 2, 6, 3, 4, 2, 3, 2, 2, 2, 11, 14, 2, 2, 58]] 883, : , [[29], [2, 2, 3, 2, 9, 16, 2, 3, 4, 5, 2, 4, 6, 10, 4, 39, 13, 2, 13, 2, 13, 39, 4, 10, 6, 4, 2, 5, 4, 3, 2, 16, 9, 2, 3, 2, 2, 58]] 887, : , FAIL 907, : , FAIL 911, : , [ [30], [10, 2, 16, 5, 2, 11, 8, 4, 5, 120, 5, 4, 8, 11, 2, 5, 16, 2, 10, 60] ] 919, : , FAIL 929, : , [[30], [4, 11, 2, 2, 6, 2, 14, 5, 4, 2, 10, 7, 4, 3, 5, 2, 5, 8, 30, 8, 5, 2, 5, 3, 4, 7, 10, 2, 4, 5, 14, 2, 6, 2, 2, 11, 4, 60]] 937, : , FAIL 941, : , [[30], [2, 2, 23, 2, 6, 2, 2, 4, 3, 2, 4, 14, 2, 11, 5, 2, 29, 2, 5, 11, 2, 14, 4, 2, 3, 4, 2, 2, 6, 2, 23, 2, 2, 60]] 947, : , FAIL 953, : , FAIL 967, : , FAIL 971, : , [[31], [12, 4, 3, 10, 2, 3, 18, 3, 248, 3, 18, 3, 2, 10, 3, 4, 12, 62]] 977, : , [[31], [7, 2, 3, 3, 5, 17, 3, 2, 61, 2, 3, 17, 5, 3, 3, 2, 7, 62]] 983, : , [[31], [5, 2, 2, 124, 2, 2, 5, 62]] 991, : , [[31], [4, 12, 20, 2, 4, 2, 3, 5, 4, 9, 8, 2, 3, 3, 6, 3, 10, 5, 2, 4, 10, 24, 2, 124, 2, 24, 10, 4, 2, 5, 10, 3, 6, 3, 3, 2, 8, 9, 4, 5, 3, 2, 4, 2, 20, 12, 4, 62]] 997, : , [[31], [3, 4, 10, 20, 2, 6, 31, 6, 2, 20, 10, 4, 3, 62]] 1009, : , [[31], [2, 3, 7, 2, 30, 2, 7, 3, 2, 62]] 1013, : , [[31], [2, 4, 2, 4, 31, 4, 2, 4, 2, 62]] 1019, : , [[31], [2, 11, 2, 3, 3, 14, 4, 4, 2, 2, 2, 2, 15, 8, 2, 2, 17, 3, 3, 17, 2, 2, 8, 15, 2, 2, 2, 2, 4, 4, 14, 3, 3, 2, 11, 2, 62]] 1021, : , FAIL 1031, : , [[32], [ 18, 6, 6, 4, 3, 9, 2, 2, 6, 3, 3, 31, 3, 3, 6, 2, 2, 9, 3, 4, 6, 6, 18, 64] ] 1033, : , FAIL 1039, : , FAIL 1049, : , FAIL 1051, : , FAIL 1061, : , [[32], [3, 4, 25, 3, 11, 10, 7, 2, 17, 2, 2, 2, 3, 4, 5, 8, 2, 15, 5, 23, 6, 2, 2, 13, 130, 13, 2, 2, 6, 23, 5, 15, 2, 8, 5, 4, 3, 2, 2, 2, 17, 2, 7, 10, 11, 3, 25, 4, 3, 64]] 1063, : , [ [32], [3, 6, 5, 14, 2, 28, 43, 4, 2, 31, 2, 4, 43, 28, 2, 14, 5, 6, 3, 64]] 1069, : , FAIL 1087, : , [[32], [2, 31, 2, 64]] 1091, : , [[33], [66]] 1093, : , [[33], [33, 66]] 1097, : , FAIL 1103, : , [[33], [9, 4, 5, 3, 3, 2, 2, 8, 4, 3, 2, 7, 3, 2, 3, 2, 47, 3, 2, 6, 4, 2, 2, 65, 2, 2, 4, 6, 2, 3, 47, 2, 3, 2, 3, 7, 2, 3, 4, 8, 2, 2, 3, 3, 5, 4, 9, 66]] 1109, : , FAIL 1117, : , [[33], [4, 2, 2, 2, 10, 4, 2, 21, 4, 9, 33, 9, 4, 21, 2, 4, 10, 2, 2, 2, 4, 66]] 1123, : , [[33], [3, 2, 10, 4, 2, 3, 3, 2, 6, 2, 2, 178, 67, 178, 2, 2, 6, 2, 3, 3, 2, 4, 10, 2, 3, 66]] 1129, : , [[33], [3, 6, 33, 6, 3, 66]] 1151, : , [[33], [2, 12, 3, 4, 2, 3, 2, 5, 2, 134, 2, 5, 2, 3, 2, 4, 3, 12, 2, 66]] 1153, : , [[33], [2, 21, 3, 29, 3, 2, 2, 2, 2, 2, 2, 12, 2, 2, 13, 8, 23, 5, 6, 7, 2, 11, 6, 26, 11, 8, 8, 8, 11, 26, 6, 11, 2, 7, 6, 5, 23, 8, 13, 2, 2, 12, 2, 2, 2, 2, 2, 2, 3, 29, 3, 21, 2, 66]] 1163, : , [[34], [19, 4, 5, 4, 3, 2, 16, 7, 7, 2, 6, 6, 3, 67, 3, 6, 6, 2, 7, 7, 16, 2, 3, 4, 5, 4, 19, 68]] 1171, : , FAIL 1181, : , [[34], [5, 4, 7, 3, 11, 2, 7, 2, 2, 54, 6, 2, 5, 16, 2, 5, 6, 3, 2, 2, 2, 2, 136, 2, 2, 2, 2, 3, 6, 5, 2, 16, 5, 2, 6, 54, 2, 2, 7, 2, 11, 3, 7, 4, 5, 68]] 1187, : , FAIL 1193, : , [[34], [3, 2, 2, 5, 13, 15, 4, 2, 3, 2, 3, 2, 3, 4, 4, 3, 137, 3, 4, 4, 3, 2, 3, 2, 3, 2, 4, 15, 13, 5, 2, 2, 3, 68]] 1201, : , FAIL 1213, : , [[34], [2, 4, 2, 4, 3, 2, 4, 9, 2, 9, 42, 3, 138, 3, 42, 9, 2, 9, 4, 2, 3, 4, 2, 4, 2, 68]] 1217, : , [[34], [2, 7, 2, 2, 2, 3, 3, 8, 4, 3, 4, 5, 3, 2, 138, 2, 3, 5, 4, 3, 4, 8, 3, 3, 2, 2, 2, 7, 2, 68]] 1223, : , [[34], [2, 33, 2, 68]] Finally, the sequence of periods (for the OEIS) is [2, 1, 2, 4, 1, 2, 2, 8, 4, 2, 8, 2, 6, 12, 4, 2, 3, 6, 20, 8, 10, 4, 1, 10, 14 , 2, 8, 12, 10, 10, 12, 3, 8, 28, 14, 36, 30, 32, 4, 2, 10, 10, 12, FAIL, 2, 16 , FAIL, 4, 1, 2, 12, 12, 7, 24, 2, FAIL, 6, 36, 34, 18, 21, 2, 10, 12, 30, 6, 13, 50, 20, 14, 22, 4, 16, 10, 52, 8, FAIL, 10, 2, FAIL, 7, FAIL, FAIL, 70, 4, 1, 52, 9, 6, 28, 10, 12, 136, 7, 12, 8, FAIL, FAIL, 36, 22, 26, 6, 5, 23, 26, 2 , 20, FAIL, FAIL, 80, FAIL, FAIL, FAIL, 30, FAIL, 34, FAIL, 28, 20, 3, FAIL, 28 , 2, 28, 13, 10, 22, 20, 4, 2, 38, 8, FAIL, 26, 10, 20, 6, 76, 6, FAIL, FAIL, 34, FAIL, 20, 26, 4, 14, 3, 42, 16, FAIL, 30, 38, FAIL, FAIL, 20, FAIL, 38, FAIL, 34, FAIL, FAIL, FAIL, 18, 18, 8, 48, 14, 10, 10, 37, FAIL, 24, FAIL, FAIL , FAIL, FAIL, 50, 20, FAIL, 4, 1, 2, FAIL, 48, FAIL, 22, 26, 6, 20, 54, 28, FAIL, 46, FAIL, 34, FAIL, 26, 30, 4] This ends this article, that took, 149.154, seconds to generate.