> hdedeuxpuisa(1,117): "*** n=2^", 1, "p_k=", 2, "nprime=", 0, "***" "nprime is smaller than p_{k+1}-p_k" "factors of G(p_k,nprime)=", [], [], [], [] 1, "ecart=", 0, "type=", 1 "*** n=2^", 2, "p_k=", 2, "nprime=", 2, "***" "nprime is greater than p_{k+1}-3" "factors of G(p_k,nprime)=", [1], [3], [], [2] 3 -, "ecart=", 1, "type=", 0 2 "*** n=2^", 3, "p_k=", 3, "nprime=", 3, "***" "nprime is greater than p_{k+1}-3" "factors of G(p_k,nprime)=", [1], [5], [], [2] 5 -, "ecart=", 0, "type=", 0 2 "*** n=2^", 4, "p_k=", 5, "nprime=", 6, "***" "nprime is greater than p_{k+1}-3" "factors of G(p_k,nprime)=", [1], [7], [], [2] 7 -, "ecart=", 1, "type=", 0 2 "*** n=2^", 5, "p_k=", 11, "nprime=", 4, "***" "The delta-method has failed, but nprime is small" "factors of G(p_k,nprime)=", [1], [13], [], [11] 13 --, "ecart=", 2, "type=", 4 11 "*** n=2^", 6, "p_k=", 17, "nprime=", 6, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [19], [], [13] 19 --, "ecart=", 0, "type=", 2 13 "*** n=2^", 7, "p_k=", 23, "nprime=", 28, "***" "nprime is greater than p_{k+1}-3" "factors of G(p_k,nprime)=", [1], [29], [], [2] 29 --, "ecart=", 1, "type=", 0 2 "*** n=2^", 8, "p_k=", 41, "nprime=", 18, "***" "The delta-method has failed, but nprime is small" "factors of G(p_k,nprime)=", [2], [47], [], [29] 47 --, "ecart=", 0, "type=", 4 29 "*** n=2^", 9, "p_k=", 61, "nprime=", 11, "***" "The delta-method has failed, but nprime is small" "factors of G(p_k,nprime)=", [2], [71], [], [61] 71 --, "ecart=", 1, "type=", 4 61 "*** n=2^", 10, "p_k=", 89, "nprime=", 61, "***" "mm=nprime - 1", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [97], [], [37] 97 --, "ecart=", 1, "type=", 2 37 "*** n=2^", 11, "p_k=", 137, "nprime=", 60, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [139], [], [79] 139 ---, "ecart=", 0, "type=", 2 79 "*** n=2^", 12, "p_k=", 197, "nprime=", 68, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [199], [], [131] 199 ---, "ecart=", 0, "type=", 2 131 "*** n=2^", 13, "p_k=", 283, "nprime=", 210, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [293], [], [83] 293 ---, "ecart=", 0, "type=", 2 83 "*** n=2^", 14, "p_k=", 431, "nprime=", 416, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [433], [], [17] 433 ---, "ecart=", 0, "type=", 2 17 "*** n=2^", 15, "p_k=", 619, "nprime=", 415, "***" "[number of q's, compdelta, compqmax]=", [3, 2, 1] "list of trialed q's=", [223, 227, 229] "list of corresponding d's=", [6, 10, 12], "delta=", 10 "factors of G(p_k,nprime)=", [1], [631], [], [223] 631 ---, "ecart=", 7, "type=", 3 223 "*** n=2^", 16, "p_k=", 919, "nprime=", 2, "***" "nprime is smaller than p_{k+1}-p_k" "factors of G(p_k,nprime)=", [], [], [], [] 1, "ecart=", 2, "type=", 1 "*** n=2^", 17, "p_k=", 1319, "nprime=", 334, "***" "[number of q's, compdelta, compqmax]=", [6, 4, 2] "list of trialed q's=", [991, 997, 1009, 1013, 1019, 1021] "list of corresponding d's=", [4, 10, 22, 26, 32, 34], "delta=", 26 "factors of G(p_k,nprime)=", [1, 2], [1321, 1327], [0], [1319, 997] 1752967 -------, "ecart=", 2, "type=", 3 1315043 "*** n=2^", 18, "p_k=", 1933, "nprime=", 922, "***" "[number of q's, compdelta, compqmax]=", [5, 5, 1] "list of trialed q's=", [1031, 1033, 1039, 1049, 1051] "list of corresponding d's=", [4, 6, 12, 22, 24], "delta=", 24 "factors of G(p_k,nprime)=", [2], [1951], [], [1031] 1951 ----, "ecart=", 2, "type=", 3 1031 "*** n=2^", 19, "p_k=", 2789, "nprime=", 2628, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [2791], [], [163] 2791 ----, "ecart=", 0, "type=", 2 163 "*** n=2^", 20, "p_k=", 4049, "nprime=", 2929, "***" "mm=nprime - 1", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [4051], [], [1123] 4051 ----, "ecart=", 1, "type=", 2 1123 "*** n=2^", 21, "p_k=", 5851, "nprime=", 5142, "***" "[number of q's, compdelta, compqmax]=", [1, 1, 1] "list of trialed q's=", [719] "list of corresponding d's=", [4], "delta=", 4 "factors of G(p_k,nprime)=", [2], [5861], [], [719] 5861 ----, "ecart=", 0, "type=", 3 719 "*** n=2^", 22, "p_k=", 8521, "nprime=", 1847, "***" "[number of q's, compdelta, compqmax]=", [3, 2, 2] "list of trialed q's=", [6689, 6691, 6701] "list of corresponding d's=", [8, 10, 20], "delta=", 10 "factors of G(p_k,nprime)=", [2], [8537], [], [6691] 8537 ----, "ecart=", 1, "type=", 3 6691 "*** n=2^", 23, "p_k=", 12269, "nprime=", 2068, "***" "[number of q's, compdelta, compqmax]=", [6, 4, 1] "list of trialed q's=", [10211, 10223, 10243, 10247, 10253, 10259] "list of corresponding d's=", [2, 14, 34, 38, 44, 50], "delta=", 38 "factors of G(p_k,nprime)=", [1], [12277], [], [10211] 12277 -----, "ecart=", 2, "type=", 3 10211 "*** n=2^", 24, "p_k=", 17657, "nprime=", 12129, "***" "mm=nprime - 1", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [17659], [], [5531] 17659 -----, "ecart=", 1, "type=", 2 5531 "*** n=2^", 25, "p_k=", 25457, "nprime=", 12848, "***" "[number of q's, compdelta, compqmax]=", [3, 2, 1] "list of trialed q's=", [12619, 12637, 12641] "list of corresponding d's=", [4, 22, 26], "delta=", 22 "factors of G(p_k,nprime)=", [1], [25463], [], [12619] 25463 -----, "ecart=", 4, "type=", 3 12619 "*** n=2^", 26, "p_k=", 36677, "nprime=", 11619, "***" "[number of q's, compdelta, compqmax]=", [1, 1, 1] "list of trialed q's=", [25073] "list of corresponding d's=", [8], "delta=", 8 "factors of G(p_k,nprime)=", [2], [36691], [], [25073] 36691 -----, "ecart=", 1, "type=", 3 25073 "*** n=2^", 27, "p_k=", 52807, "nprime=", 46278, "***" "[number of q's, compdelta, compqmax]=", [6, 5, 1] "list of trialed q's=", [6547, 6551, 6553, 6563, 6569, 6571] "list of corresponding d's=", [12, 16, 18, 28, 34, 36], "delta=", 34 "factors of G(p_k,nprime)=", [1, 2], [52813, 52817], [0], [52807, 6547] 2789424221 ----------, "ecart=", 2, "type=", 3 345727429 "*** n=2^", 28, "p_k=", 75937, "nprime=", 22242, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [75941], [], [53699] 75941 -----, "ecart=", 0, "type=", 2 53699 "*** n=2^", 29, "p_k=", 109159, "nprime=", 55375, "***" "[number of q's, compdelta, compqmax]=", [2, 2, 1] "list of trialed q's=", [53813, 53819] "list of corresponding d's=", [18, 24], "delta=", 24 "factors of G(p_k,nprime)=", [1, 2], [109169, 109171], [0], [109159, 53813] 11918088899 -----------, "ecart=", 7, "type=", 3 5874173267 "*** n=2^", 30, "p_k=", 156799, "nprime=", 9189, "***" "mm=nprime - 1", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [156817], [], [147629] 156817 ------, "ecart=", 1, "type=", 2 147629 "*** n=2^", 31, "p_k=", 225263, "nprime=", 52318, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [225287], [], [172969] 225287 ------, "ecart=", 0, "type=", 2 172969 "*** n=2^", 32, "p_k=", 323377, "nprime=", 125320, "***" "[number of q's, compdelta, compqmax]=", [1, 1, 1] "list of trialed q's=", [198073] "list of corresponding d's=", [12], "delta=", 12 "factors of G(p_k,nprime)=", [1, 2], [323381, 323383], [-1], [323371, 198073] 104575917923 ------------, "ecart=", 0, "type=", 3 64051064083 "*** n=2^", 33, "p_k=", 464437, "nprime=", 188704, "***" "[number of q's, compdelta, compqmax]=", [3, 2, 1] "list of trialed q's=", [275767, 275773, 275783] "list of corresponding d's=", [24, 30, 40], "delta=", 30 "factors of G(p_k,nprime)=", [1, 2], [464447, 464459], [0], [464437, 275767] 215716589173 ------------, "ecart=", 2, "type=", 3 128076398179 "*** n=2^", 34, "p_k=", 665789, "nprime=", 42158, "***" "[number of q's, compdelta, compqmax]=", [6, 2, 2] "list of trialed q's=", [623653, 623669, 623671, 623677, 623681, 623683] "list of corresponding d's=", [10, 26, 28, 34, 38, 40], "delta=", 26 "factors of G(p_k,nprime)=", [2, 3], [665803, 665813], [0], [665789, 623669] 443300292839 ------------, "ecart=", 0, "type=", 3 415231959841 "*** n=2^", 35, "p_k=", 954469, "nprime=", 910863, "***" "[number of q's, compdelta, compqmax]=", [5, 5, 1] "list of trialed q's=", [43633, 43649, 43651, 43661, 43669] "list of corresponding d's=", [4, 20, 22, 32, 40], "delta=", 40 "factors of G(p_k,nprime)=", [1], [954491], [], [43633] 954491 ------, "ecart=", 5, "type=", 3 43633 "*** n=2^", 36, "p_k=", 1368229, "nprime=", 1313452, "***" "[number of q's, compdelta, compqmax]=", [2, 2, 1] "list of trialed q's=", [54787, 54799] "list of corresponding d's=", [6, 18], "delta=", 18 "factors of G(p_k,nprime)=", [1], [1368233], [], [54787] 1368233 -------, "ecart=", 6, "type=", 3 54787 "*** n=2^", 37, "p_k=", 1959739, "nprime=", 56059, "***" "[number of q's, compdelta, compqmax]=", [6, 3, 3] "list of trialed q's=", [1903703, 1903709, 1903747, 1903757, 1903787, 1903789] "list of corresponding d's=", [10, 16, 54, 64, 94, 96], "delta=", 54 "factors of G(p_k,nprime)=", [1, 2], [1959751, 1959773], [-3], [1959719, 1903747] 3840667096523 -------------, "ecart=", 1, "type=", 3 3730809167093 "*** n=2^", 38, "p_k=", 2807477, "nprime=", 340473, "***" "[number of q's, compdelta, compqmax]=", [9, 7, 7] "list of trialed q's=", [2467013, 2467019, 2467021, 2467027, 2467033, 2467043, 2467051, 2467061, 2467103] "list of corresponding d's=", [6, 12, 14, 20, 26, 36, 44, 54, 96], "delta=", 44 "factors of G(p_k,nprime)=", [1, 2], [2807479, 2807521], [0], [2807477, 2467051] 7882056249559 -------------, "ecart=", 1, "type=", 3 6926188940327 "*** n=2^", 39, "p_k=", 4019809, "nprime=", 1222039, "***" "mm=nprime - 1", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [4019831], [], [2797793] 4019831 -------, "ecart=", 1, "type=", 2 2797793 "*** n=2^", 40, "p_k=", 5753453, "nprime=", 4612647, "***" "[number of q's, compdelta, compqmax]=", [2, 1, 1] "list of trialed q's=", [1140847, 1140851] "list of corresponding d's=", [26, 30], "delta=", 26 "factors of G(p_k,nprime)=", [1, 2], [5753467, 5753479], [0], [5753453, 1140847] 33102451561693 --------------, "ecart=", 1, "type=", 3 6563809594691 "*** n=2^", 41, "p_k=", 8232613, "nprime=", 5678746, "***" "[number of q's, compdelta, compqmax]=", [6, 5, 1] "list of trialed q's=", [2553917, 2553937, 2553949, 2553959, 2554003, 2554007] "list of corresponding d's=", [4, 24, 36, 46, 90, 94], "delta=", 90 "factors of G(p_k,nprime)=", [1], [8232659], [], [2553917] 8232659 -------, "ecart=", 4, "type=", 3 2553917 "*** n=2^", 42, "p_k=", 11776829, "nprime=", 10786702, "***" "[number of q's, compdelta, compqmax]=", [5, 5, 1] "list of trialed q's=", [990163, 990169, 990179, 990181, 990211] "list of corresponding d's=", [6, 12, 22, 24, 54], "delta=", 54 "factors of G(p_k,nprime)=", [2], [11776861], [], [990163] 11776861 --------, "ecart=", 4, "type=", 3 990163 "*** n=2^", 43, "p_k=", 16843297, "nprime=", 2478963, "***" "[number of q's, compdelta, compqmax]=", [7, 5, 1] "list of trialed q's=", [14364353, 14364359, 14364373, 14364379, 14364403, 14364409, 14364433] "list of corresponding d's=", [2, 8, 22, 28, 52, 58, 82], "delta=", 52 "factors of G(p_k,nprime)=", [1], [16843313], [], [14364353] 16843313 --------, "ecart=", 3, "type=", 3 14364353 "*** n=2^", 44, "p_k=", 24082589, "nprime=", 2282340, "***" "[number of q's, compdelta, compqmax]=", [3, 2, 2] "list of trialed q's=", [21800281, 21800291, 21800293] "list of corresponding d's=", [14, 24, 26], "delta=", 24 "factors of G(p_k,nprime)=", [1, 3], [24082607, 24082613], [0], [24082589, 21800291] 579972104412091 ---------------, "ecart=", 0, "type=", 3 525007448233399 "*** n=2^", 45, "p_k=", 34426313, "nprime=", 21040805, "***" "[number of q's, compdelta, compqmax]=", [4, 3, 1] "list of trialed q's=", [13385531, 13385543, 13385573, 13385587] "list of corresponding d's=", [14, 26, 56, 70], "delta=", 56 "factors of G(p_k,nprime)=", [1], [34426321], [], [13385531] 34426321 --------, "ecart=", 15, "type=", 3 13385531 "*** n=2^", 46, "p_k=", 49198559, "nprime=", 45448874, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [49198573], [], [3749699] 49198573 --------, "ecart=", 0, "type=", 2 3749699 "*** n=2^", 47, "p_k=", 70292291, "nprime=", 29290709, "***" "[number of q's, compdelta, compqmax]=", [11, 8, 2] "list of trialed q's=", [41001613, 41001619, 41001629, 41001641, 41001647, 41001683, 41001689, 41001707, 41001713, 41001733, 41001743] "list of corresponding d's=", [12, 18, 28, 40, 46, 82, 88, 106, 112, 132, 142], "delta=", 106 "factors of G(p_k,nprime)=", [2], [70292323], [], [41001619] 70292323 --------, "ecart=", 5, "type=", 3 41001619 "*** n=2^", 48, "p_k=", 100416713, "nprime=", 88527836, "***" "[number of q's, compdelta, compqmax]=", [1, 1, 1] "list of trialed q's=", [11888909] "list of corresponding d's=", [24], "delta=", 24 "factors of G(p_k,nprime)=", [1, 2], [100416721, 100416727], [-1], [100416703, 11888909] 10083518458892167 -----------------, "ecart=", 0, "type=", 3 1193845044047027 "*** n=2^", 49, "p_k=", 143413759, "nprime=", 57216853, "***" "mm=nprime - 1", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [143413789], [], [86196937] 143413789 ---------, "ecart=", 1, "type=", 2 86196937 "*** n=2^", 50, "p_k=", 204789517, "nprime=", 102090071, "***" "[number of q's, compdelta, compqmax]=", [6, 5, 1] "list of trialed q's=", [102699461, 102699511, 102699517, 102699551, 102699593, 102699631] "list of corresponding d's=", [8, 58, 64, 98, 140, 178], "delta=", 140 "factors of G(p_k,nprime)=", [1], [204789523], [], [102699461] 204789523 ---------, "ecart=", 9, "type=", 3 102699461 "*** n=2^", 51, "p_k=", 292368871, "nprime=", 267431603, "***" "[number of q's, compdelta, compqmax]=", [2, 2, 1] "list of trialed q's=", [24937277, 24937301] "list of corresponding d's=", [2, 26], "delta=", 26 "factors of G(p_k,nprime)=", [1], [292368877], [], [24937277] 292368877 ---------, "ecart=", 3, "type=", 3 24937277 "*** n=2^", 52, "p_k=", 417329221, "nprime=", 342115280, "***" "[number of q's, compdelta, compqmax]=", [7, 7, 1] "list of trialed q's=", [75213973, 75213991, 75213997, 75214003, 75214021, 75214039, 75214057] "list of corresponding d's=", [4, 22, 28, 34, 52, 70, 88], "delta=", 88 "factors of G(p_k,nprime)=", [1], [417329249], [], [75213973] 417329249 ---------, "ecart=", 4, "type=", 3 75213973 "*** n=2^", 53, "p_k=", 595600669, "nprime=", 413704712, "***" "[number of q's, compdelta, compqmax]=", [4, 4, 1] "list of trialed q's=", [181895993, 181896017, 181896023, 181896031] "list of corresponding d's=", [32, 56, 62, 70], "delta=", 70 "factors of G(p_k,nprime)=", [3], [595600703], [], [181895993] 595600703 ---------, "ecart=", 2, "type=", 3 181895993 "*** n=2^", 54, "p_k=", 849875249, "nprime=", 803469692, "***" "[number of q's, compdelta, compqmax]=", [3, 3, 1] "list of trialed q's=", [46405573, 46405609, 46405613] "list of corresponding d's=", [14, 50, 54], "delta=", 54 "factors of G(p_k,nprime)=", [1], [849875251], [], [46405573] 849875251 ---------, "ecart=", 14, "type=", 3 46405573 "*** n=2^", 55, "p_k=", 1212532679, "nprime=", 649377128, "***" "[number of q's, compdelta, compqmax]=", [4, 2, 1] "list of trialed q's=", [563155559, 563155591, 563155597, 563155601] "list of corresponding d's=", [6, 38, 44, 48], "delta=", 38 "factors of G(p_k,nprime)=", [1], [1212532681], [], [563155559] 1212532681 ----------, "ecart=", 6, "type=", 3 563155559 "*** n=2^", 56, "p_k=", 1729634189, "nprime=", 1133374585, "***" "[number of q's, compdelta, compqmax]=", [8, 6, 1] "list of trialed q's=", [596259667, 596259701, 596259709, 596259739, 596259827, 596259857, 596259871, 596259901] "list of corresponding d's=", [18, 52, 60, 90, 178, 208, 222, 252], "delta=", 208 "factors of G(p_k,nprime)=", [1], [1729634233], [], [596259667] 1729634233 ----------, "ecart=", 19, "type=", 3 596259667 "*** n=2^", 57, "p_k=", 2466937619, "nprime=", 830682139, "***" "[number of q's, compdelta, compqmax]=", [5, 4, 1] "list of trialed q's=", [1636255493, 1636255499, 1636255529, 1636255549, 1636255561] "list of corresponding d's=", [10, 16, 46, 66, 78], "delta=", 66 "factors of G(p_k,nprime)=", [1], [2466937621], [], [1636255493] 2466937621 ----------, "ecart=", 11, "type=", 3 1636255493 "*** n=2^", 58, "p_k=", 3517968721, "nprime=", 148045078, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [3517968737], [], [3369923659] 3517968737 ----------, "ecart=", 0, "type=", 2 3369923659 "*** n=2^", 59, "p_k=", 5016124667, "nprime=", 3838405139, "***" "[number of q's, compdelta, compqmax]=", [11, 9, 1] "list of trialed q's=", [1177719593, 1177719601, 1177719649, 1177719661, 1177719677, 1177719689, 1177719701, 1177719707, 1177719773, 1177719797, 1177719799] "list of corresponding d's=", [4, 12, 60, 72, 88, 100, 112, 118, 184, 208, 210], "delta=", 184 "factors of G(p_k,nprime)=", [1], [5016124727], [], [1177719593] 5016124727 ----------, "ecart=", 5, "type=", 3 1177719593 "*** n=2^", 60, "p_k=", 7151293243, "nprime=", 2259746163, "***" "[number of q's, compdelta, compqmax]=", [7, 5, 1] "list of trialed q's=", [4891547159, 4891547183, 4891547197, 4891547237, 4891547251, 4891547267, 4891547291] "list of corresponding d's=", [20, 44, 58, 98, 112, 128, 152], "delta=", 112 "factors of G(p_k,nprime)=", [2], [7151293313], [], [4891547159] 7151293313 ----------, "ecart=", 9, "type=", 3 4891547159 "*** n=2^", 61, "p_k=", 10193990659, "nprime=", 5198647657, "***" "[number of q's, compdelta, compqmax]=", [5, 2, 1] "list of trialed q's=", [4995343033, 4995343091, 4995343097, 4995343099, 4995343103] "list of corresponding d's=", [26, 84, 90, 92, 96], "delta=", 84 "factors of G(p_k,nprime)=", [1, 2], [10193990663, 10193990683], [0], [10193990659, 4995343033] 103917445841210992829 ---------------------, "ecart=", 3, "type=", 3 50922480216902728747 "*** n=2^", 62, "p_k=", 14529489427, "nprime=", 10108557436, "***" "[number of q's, compdelta, compqmax]=", [5, 4, 1] "list of trialed q's=", [4420932007, 4420932011, 4420932067, 4420932101, 4420932107] "list of corresponding d's=", [6, 10, 66, 100, 106], "delta=", 100 "factors of G(p_k,nprime)=", [1], [14529489437], [], [4420932007] 14529489437 -----------, "ecart=", 6, "type=", 3 4420932007 "*** n=2^", 63, "p_k=", 20706267137, "nprime=", 3577204465, "***" "[number of q's, compdelta, compqmax]=", [5, 3, 1] "list of trialed q's=", [17129062693, 17129062703, 17129062763, 17129062777, 17129062789] "list of corresponding d's=", [6, 16, 76, 90, 102], "delta=", 76 "factors of G(p_k,nprime)=", [1], [20706267151], [], [17129062693] 20706267151 -----------, "ecart=", 7, "type=", 3 17129062693 "*** n=2^", 64, "p_k=", 29505444469, "nprime=", 16168326584, "***" "[number of q's, compdelta, compqmax]=", [3, 3, 1] "list of trialed q's=", [13337117909, 13337117953, 13337117957] "list of corresponding d's=", [2, 46, 50], "delta=", 50 "factors of G(p_k,nprime)=", [1], [29505444491], [], [13337117909] 29505444491 -----------, "ecart=", 2, "type=", 3 13337117909 "*** n=2^", 65, "p_k=", 42038976929, "nprime=", 33826102762, "***" "[number of q's, compdelta, compqmax]=", [7, 6, 1] "list of trialed q's=", [8212874291, 8212874303, 8212874309, 8212874381, 8212874387, 8212874389, 8212874401] "list of corresponding d's=", [22, 34, 40, 112, 118, 120, 132], "delta=", 120 "factors of G(p_k,nprime)=", [4], [42038977049], [], [8212874291] 42038977049 -----------, "ecart=", 4, "type=", 3 8212874291 "*** n=2^", 66, "p_k=", 59889909799, "nprime=", 21572996461, "***" "[number of q's, compdelta, compqmax]=", [4, 3, 3] "list of trialed q's=", [38316913403, 38316913421, 38316913429, 38316913469] "list of corresponding d's=", [24, 42, 50, 90], "delta=", 50 "factors of G(p_k,nprime)=", [2], [59889909889], [], [38316913429] 59889909889 -----------, "ecart=", 1, "type=", 3 38316913429 "*** n=2^", 67, "p_k=", 85311533303, "nprime=", 26304530075, "***" "[number of q's, compdelta, compqmax]=", [6, 3, 1] "list of trialed q's=", [59007003239, 59007003257, 59007003299, 59007003311, 59007003317, 59007003343] "list of corresponding d's=", [2, 20, 62, 74, 80, 106], "delta=", 62 "factors of G(p_k,nprime)=", [1], [85311533311], [], [59007003239] 85311533311 -----------, "ecart=", 3, "type=", 3 59007003239 "*** n=2^", 68, "p_k=", 121511451227, "nprime=", 91095475794, "***" "[number of q's, compdelta, compqmax]=", [7, 7, 1] "list of trialed q's=", [30415975453, 30415975463, 30415975477, 30415975483, 30415975487, 30415975517, 30415975549] "list of corresponding d's=", [14, 24, 38, 44, 48, 78, 110], "delta=", 110 "factors of G(p_k,nprime)=", [1], [121511451233], [], [30415975453] 121511451233 ------------, "ecart=", 14, "type=", 3 30415975453 "*** n=2^", 69, "p_k=", 173053904629, "nprime=", 130748031024, "***" "[number of q's, compdelta, compqmax]=", [3, 2, 1] "list of trialed q's=", [42305873639, 42305873669, 42305873671] "list of corresponding d's=", [6, 36, 38], "delta=", 36 "factors of G(p_k,nprime)=", [2], [173053904659], [], [42305873639] 173053904659 ------------, "ecart=", 4, "type=", 3 42305873639 "*** n=2^", 70, "p_k=", 246435048317, "nprime=", 220789910868, "***" "[number of q's, compdelta, compqmax]=", [6, 6, 1] "list of trialed q's=", [25645137487, 25645137491, 25645137499, 25645137503, 25645137527, 25645137569] "list of corresponding d's=", [14, 18, 26, 30, 54, 96], "delta=", 96 "factors of G(p_k,nprime)=", [1], [246435048341], [], [25645137487] 246435048341 ------------, "ecart=", 14, "type=", 3 25645137487 "*** n=2^", 71, "p_k=", 350898854197, "nprime=", 63149630811, "***" "[number of q's, compdelta, compqmax]=", [10, 6, 1] "list of trialed q's=", [287749223401, 287749223413, 287749223429, 287749223477, 287749223483, 287749223519, 287749223539, 287749223543, 287749223603, 287749223611] "list of corresponding d's=", [2, 14, 30, 78, 84, 120, 140, 144, 204, 212], "delta=", 120 "factors of G(p_k,nprime)=", [1], [350898854209], [], [287749223401] 350898854209 ------------, "ecart=", 3, "type=", 3 287749223401 "*** n=2^", 72, "p_k=", 499598330159, "nprime=", 453777514684, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [499598330237], [], [45820815553] 499598330237 ------------, "ecart=", 0, "type=", 2 45820815553 "*** n=2^", 73, "p_k=", 711246472639, "nprime=", 246093977943, "***" "[number of q's, compdelta, compqmax]=", [8, 5, 1] "list of trialed q's=", [465152494727, 465152494747, 465152494811, 465152494823, 465152494901, 465152494907, 465152494909, 465152494943] "list of corresponding d's=", [2, 22, 86, 98, 176, 182, 184, 218], "delta=", 176 "factors of G(p_k,nprime)=", [1], [711246472667], [], [465152494727] 711246472667 ------------, "ecart=", 3, "type=", 3 465152494727 "*** n=2^", 74, "p_k=", 1012466288003, "nprime=", 393105146011, "***" "mm=nprime - 1", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [1012466288017], [], [619361142007] 1012466288017 -------------, "ecart=", 1, "type=", 2 619361142007 "*** n=2^", 75, "p_k=", 1441131375731, "nprime=", 606145831006, "***" "[number of q's, compdelta, compqmax]=", [6, 3, 1] "list of trialed q's=", [834985544753, 834985544807, 834985544821, 834985544839, 834985544849, 834985544857] "list of corresponding d's=", [22, 76, 90, 108, 118, 126], "delta=", 90 "factors of G(p_k,nprime)=", [2], [1441131375757], [], [834985544753] 1441131375757 -------------, "ecart=", 2, "type=", 3 834985544753 "*** n=2^", 76, "p_k=", 2051115029477, "nprime=", 1673698573035, "***" "[number of q's, compdelta, compqmax]=", [1, 1, 1] "list of trialed q's=", [377416456517] "list of corresponding d's=", [54], "delta=", 54 "factors of G(p_k,nprime)=", [1, 4], [2051115029497, 2051115029527], [-1], [2051115029473, 377416456517] 4207072864290012630957919 -------------------------, "ecart=", 1, "type=", 3 774124566332461677925541 "*** n=2^", 77, "p_k=", 2919047298757, "nprime=", 2804477424618, "***" "[number of q's, compdelta, compqmax]=", [8, 8, 1] "list of trialed q's=", [114569874187, 114569874191, 114569874233, 114569874247, 114569874259, 114569874329, 114569874337, 114569874371] "list of corresponding d's=", [32, 36, 78, 92, 104, 174, 182, 216], "delta=", 216 "factors of G(p_k,nprime)=", [1], [2919047298773], [], [114569874187] 2919047298773 -------------, "ecart=", 32, "type=", 3 114569874187 "*** n=2^", 78, "p_k=", 4153913403373, "nprime=", 787915533962, "***" "[number of q's, compdelta, compqmax]=", [3, 1, 1] "list of trialed q's=", [3365997869449, 3365997869461, 3365997869471] "list of corresponding d's=", [28, 40, 50], "delta=", 28 "factors of G(p_k,nprime)=", [1, 2], [4153913403383, 4153913403401], [0], [4153913403373, 3365997869449] 17254996562879708517105583 --------------------------, "ecart=", 0, "type=", 3 13982063665629162530251477 "*** n=2^", 79, "p_k=", 5910713670031, "nprime=", 1759543655792, "***" "[number of q's, compdelta, compqmax]=", [6, 5, 2] "list of trialed q's=", [4151170014287, 4151170014301, 4151170014323, 4151170014337, 4151170014359, 4151170014367] "list of corresponding d's=", [26, 40, 62, 76, 98, 106], "delta=", 98 "factors of G(p_k,nprime)=", [1, 2], [5910713670053, 5910713670061], [0], [5910713670031, 4151170014301] 34936536089398690258383233 --------------------------, "ecart=", 10, "type=", 3 24536377350151702465113331 "*** n=2^", 80, "p_k=", 8409873290459, "nprime=", 1976700506884, "***" "[number of q's, compdelta, compqmax]=", [3, 1, 1] "list of trialed q's=", [6433172783659, 6433172783677, 6433172783689] "list of corresponding d's=", [34, 52, 64], "delta=", 34 "factors of G(p_k,nprime)=", [3], [8409873290543], [], [6433172783659] 8409873290543 -------------, "ecart=", 0, "type=", 3 6433172783659 "*** n=2^", 81, "p_k=", 11964838507781, "nprime=", 11223571927097, "***" "[number of q's, compdelta, compqmax]=", [7, 7, 1] "list of trialed q's=", [741266580701, 741266580731, 741266580739, 741266580751, 741266580763, 741266580793, 741266580841] "list of corresponding d's=", [4, 34, 42, 54, 66, 96, 144], "delta=", 144 "factors of G(p_k,nprime)=", [1], [11964838507793], [], [741266580701] 11964838507793 --------------, "ecart=", 5, "type=", 3 741266580701 "*** n=2^", 82, "p_k=", 17021306080813, "nprime=", 330323646390, "***" "[number of q's, compdelta, compqmax]=", [4, 2, 2] "list of trialed q's=", [16690982434457, 16690982434487, 16690982434531, 16690982434537] "list of corresponding d's=", [30, 60, 104, 110], "delta=", 60 "factors of G(p_k,nprime)=", [1, 3], [17021306080817, 17021306080859], [-1], [17021306080799, 16690982434487] 289724860697572675390781803 ---------------------------, "ecart=", 0, "type=", 3 284102320806642869746115113 "*** n=2^", 83, "p_k=", 24212985402113, "nprime=", 12145573107408, "***" "[number of q's, compdelta, compqmax]=", [1, 1, 1] "list of trialed q's=", [12067412294741] "list of corresponding d's=", [10], "delta=", 10 "factors of G(p_k,nprime)=", [2], [24212985402149], [], [12067412294741] 24212985402149 --------------, "ecart=", 0, "type=", 3 12067412294741 "*** n=2^", 84, "p_k=", 34440851298773, "nprime=", 11341905109330, "***" "[number of q's, compdelta, compqmax]=", [6, 3, 1] "list of trialed q's=", [23098946189461, 23098946189467, 23098946189551, 23098946189581, 23098946189591, 23098946189603] "list of corresponding d's=", [12, 18, 102, 132, 142, 154], "delta=", 102 "factors of G(p_k,nprime)=", [1], [34440851298779], [], [23098946189461] 34440851298779 --------------, "ecart=", 12, "type=", 3 23098946189461 "*** n=2^", 85, "p_k=", 48985800814999, "nprime=", 11062144781712, "***" "[number of q's, compdelta, compqmax]=", [4, 2, 1] "list of trialed q's=", [37923656033327, 37923656033359, 37923656033363, 37923656033371] "list of corresponding d's=", [30, 62, 66, 74], "delta=", 62 "factors of G(p_k,nprime)=", [2, 3], [48985800815011, 48985800815023], [0], [48985800814999, 37923656033327] 2399608681488520181452710253 ----------------------------, "ecart=", 4, "type=", 3 1857720660625091500105471673 "*** n=2^", 86, "p_k=", 69668758192043, "nprime=", 29031345531597, "***" "[number of q's, compdelta, compqmax]=", [2, 1, 1] "list of trialed q's=", [40637412660497, 40637412660511] "list of corresponding d's=", [30, 44], "delta=", 30 "factors of G(p_k,nprime)=", [1, 2], [69668758192063, 69668758192073], [0], [69668758192043, 40637412660497] 4853735868024842059978116599 ----------------------------, "ecart=", 1, "type=", 3 2831158076194432292285825371 "*** n=2^", 87, "p_k=", 99078196477573, "nprime=", 37956250152266, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [99078196477609], [], [61121946325343] 99078196477609 --------------, "ecart=", 0, "type=", 2 61121946325343 "*** n=2^", 88, "p_k=", 140893471551149, "nprime=", 112612550390062, "***" "[number of q's, compdelta, compqmax]=", [6, 5, 1] "list of trialed q's=", [28280921161139, 28280921161147, 28280921161249, 28280921161271, 28280921161279, 28280921161289] "list of corresponding d's=", [38, 46, 148, 170, 178, 188], "delta=", 178 "factors of G(p_k,nprime)=", [1], [140893471551163], [], [28280921161139] 140893471551163 ---------------, "ecart=", 38, "type=", 3 28280921161139 "*** n=2^", 89, "p_k=", 200344335550459, "nprime=", 52369382699130, "***" "[number of q's, compdelta, compqmax]=", [6, 4, 2] "list of trialed q's=", [147974952851449, 147974952851461, 147974952851507, 147974952851519, 147974952851569, 147974952851603] "list of corresponding d's=", [78, 90, 136, 148, 198, 232], "delta=", 148 "factors of G(p_k,nprime)=", [3], [200344335550589], [], [147974952851461] 200344335550589 ---------------, "ecart=", 2, "type=", 3 147974952851461 "*** n=2^", 90, "p_k=", 284863767904379, "nprime=", 284252006676246, "***" "[number of q's, compdelta, compqmax]=", [5, 5, 1] "list of trialed q's=", [611761228193, 611761228219, 611761228223, 611761228237, 611761228241] "list of corresponding d's=", [12, 38, 42, 56, 60], "delta=", 60 "factors of G(p_k,nprime)=", [1], [284863767904427], [], [611761228193] 284863767904427 ---------------, "ecart=", 12, "type=", 3 611761228193 "*** n=2^", 91, "p_k=", 405015743379671, "nprime=", 273696384133842, "***" "[number of q's, compdelta, compqmax]=", [9, 7, 1] "list of trialed q's=", [131319359245897, 131319359245913, 131319359245933, 131319359245939, 131319359245951, 131319359245957, 131319359246051, 131319359246077, 131319359246081] "list of corresponding d's=", [38, 54, 74, 80, 92, 98, 192, 218, 222], "delta=", 192 "factors of G(p_k,nprime)=", [2], [405015743379713], [], [131319359245897] 405015743379713 ---------------, "ecart=", 26, "type=", 3 131319359245897 "*** n=2^", 92, "p_k=", 575813320142441, "nprime=", 252513156113169, "***" "[number of q's, compdelta, compqmax]=", [4, 3, 1] "list of trialed q's=", [323300164029289, 323300164029317, 323300164029383, 323300164029397] "list of corresponding d's=", [14, 42, 108, 122], "delta=", 108 "factors of G(p_k,nprime)=", [1, 3], [575813320142443, 575813320142453], [0], [575813320142441, 323300164029289] 331560979653469311635011432679 ------------------------------, "ecart=", 3, "type=", 3 186160540852300674993975954449 "*** n=2^", 93, "p_k=", 818591311846669, "nprime=", 542609494740313, "***" "[number of q's, compdelta, compqmax]=", [5, 3, 1] "list of trialed q's=", [275981817106409, 275981817106427, 275981817106529, 275981817106537, 275981817106553] "list of corresponding d's=", [24, 42, 144, 152, 168], "delta=", 144 "factors of G(p_k,nprime)=", [1], [818591311846697], [], [275981817106409] 818591311846697 ---------------, "ecart=", 25, "type=", 3 275981817106409 "*** n=2^", 94, "p_k=", 1163666945148943, "nprime=", 848850227750354, "***" "[number of q's, compdelta, compqmax]=", [5, 5, 1] "list of trialed q's=", [314816717398753, 314816717398763, 314816717398793, 314816717398847, 314816717398877] "list of corresponding d's=", [4, 14, 44, 98, 128], "delta=", 128 "factors of G(p_k,nprime)=", [1], [1163666945149103], [], [314816717398753] 1163666945149103 ----------------, "ecart=", 4, "type=", 3 314816717398753 "*** n=2^", 95, "p_k=", 1654119631980029, "nprime=", 1417695125364628, "***" "[number of q's, compdelta, compqmax]=", [9, 8, 1] "list of trialed q's=", [236424506615441, 236424506615447, 236424506615489, 236424506615611, 236424506615641, 236424506615677, 236424506615699, 236424506615719, 236424506615729] "list of corresponding d's=", [22, 28, 70, 192, 222, 258, 280, 300, 310], "delta=", 300 "factors of G(p_k,nprime)=", [2], [1654119631980061], [], [236424506615441] 1654119631980061 ----------------, "ecart=", 8, "type=", 3 236424506615441 "*** n=2^", 96, "p_k=", 2351160427227343, "nprime=", 764139511665826, "***" "[number of q's, compdelta, compqmax]=", [7, 3, 2] "list of trialed q's=", [1587020915561639, 1587020915561713, 1587020915561791, 1587020915561857, 1587020915561869, 1587020915561881, 1587020915561891] "list of corresponding d's=", [104, 178, 256, 322, 334, 346, 356], "delta=", 256 "factors of G(p_k,nprime)=", [1, 2], [2351160427227361, 2351160427227397], [-6], [2351160427227229, 1587020915561713] 5527955354560031342513367209317 -------------------------------, "ecart=", 10, "type=", 3 3731340773850625257553623483277 "*** n=2^", 97, "p_k=", 3341759674235299, "nprime=", 1909623792272991, "***" "[number of q's, compdelta, compqmax]=", [3, 3, 1] "list of trialed q's=", [1432135881962339, 1432135881962407, 1432135881962441] "list of corresponding d's=", [12, 80, 114], "delta=", 114 "factors of G(p_k,nprime)=", [1], [3341759674235317], [], [1432135881962339] 3341759674235317 ----------------, "ecart=", 13, "type=", 3 1432135881962339 "*** n=2^", 98, "p_k=", 4749481664698139, "nprime=", 4557540044699731, "***" "[number of q's, compdelta, compqmax]=", [4, 4, 1] "list of trialed q's=", [191941619998451, 191941619998487, 191941619998561, 191941619998631] "list of corresponding d's=", [18, 54, 128, 198], "delta=", 198 "factors of G(p_k,nprime)=", [1], [4749481664698163], [], [191941619998451] 4749481664698163 ----------------, "ecart=", 19, "type=", 3 191941619998451 "*** n=2^", 99, "p_k=", 6749874763859599, "nprime=", 5415322522313957, "***" "[number of q's, compdelta, compqmax]=", [8, 4, 1] "list of trialed q's=", [1334552241545689, 1334552241545693, 1334552241545711, 1334552241545959, 1334552241545969, 1334552241545981, 1334552241545993, 1334552241546001] "list of corresponding d's=", [42, 46, 64, 312, 322, 334, 346, 354], "delta=", 312 "factors of G(p_k,nprime)=", [1], [6749874763859603], [], [1334552241545689] 6749874763859603 ----------------, "ecart=", 43, "type=", 3 1334552241545689 "*** n=2^", 100, "p_k=", 9592330540937003, "nprime=", 2077789589606763, "***" "[number of q's, compdelta, compqmax]=", [7, 6, 1] "list of trialed q's=", [7514540951330291, 7514540951330311, 7514540951330323, 7514540951330327, 7514540951330407, 7514540951330411, 7514540951330453] "list of corresponding d's=", [12, 32, 44, 48, 128, 132, 174], "delta=", 132 "factors of G(p_k,nprime)=", [1], [9592330540937041], [], [7514540951330291] 9592330540937041 ----------------, "ecart=", 13, "type=", 3 7514540951330291 "*** n=2^", 101, "p_k=", 13631131151055013, "nprime=", 2714875794432079, "***" "[number of q's, compdelta, compqmax]=", [12, 8, 1] "list of trialed q's=", [10916255356622969, 10916255356623011, 10916255356623049, 10916255356623059, 10916255356623103, 10916255356623107, 10916255356623109, 10916255356623181, 10916255356623191, 10916255356623223, 10916255356623293, 10916255356623301] "list of corresponding d's=", [18, 60, 98, 108, 152, 156, 158, 230, 240, 272, 342, 350], "delta=", 230 "factors of G(p_k,nprime)=", [1], [13631131151055029], [], [10916255356622969] 13631131151055029 -----------------, "ecart=", 19, "type=", 3 10916255356622969 "*** n=2^", 102, "p_k=", 19369544065478017, "nprime=", 10123908719389466, "***" "[number of q's, compdelta, compqmax]=", [7, 5, 1] "list of trialed q's=", [9245635346088643, 9245635346088677, 9245635346088719, 9245635346088763, 9245635346088833, 9245635346088857, 9245635346088881] "list of corresponding d's=", [28, 62, 104, 148, 218, 242, 266], "delta=", 218 "factors of G(p_k,nprime)=", [2], [19369544065478083], [], [9245635346088643] 19369544065478083 -----------------, "ecart=", 26, "type=", 3 9245635346088643 "*** n=2^", 103, "p_k=", 27522446269314197, "nprime=", 1548737012611438, "***" "[number of q's, compdelta, compqmax]=", [6, 5, 5] "list of trialed q's=", [25973709256702783, 25973709256702817, 25973709256702843, 25973709256702847, 25973709256702897, 25973709256703029] "list of corresponding d's=", [12, 46, 72, 76, 126, 258], "delta=", 126 "factors of G(p_k,nprime)=", [1, 2], [27522446269314209, 27522446269314289], [-1], [27522446269314163, 25973709256702897] 757485048647289822796272714432401 ---------------------------------, "ecart=", 0, "type=", 3 714860017432393389200354845230211 "*** n=2^", 104, "p_k=", 39105260093248747, "nprime=", 36643908758087768, "***" "[number of q's, compdelta, compqmax]=", [4, 4, 1] "list of trialed q's=", [2461351335161051, 2461351335161053, 2461351335161071, 2461351335161099] "list of corresponding d's=", [68, 70, 88, 116], "delta=", 116 "factors of G(p_k,nprime)=", [1, 3], [39105260093248751, 39105260093248813], [0], [39105260093248747, 2461351335161051] 1529221366960635738281975344482563 ----------------------------------, "ecart=", 2, "type=", 3 96251784142337969158805048953097 "*** n=2^", 105, "p_k=", 55560252023842141, "nprime=", 17911529241757605, "***" "[number of q's, compdelta, compqmax]=", [11, 8, 2] "list of trialed q's=", [37648722782084621, 37648722782084629, 37648722782084657, 37648722782084669, 37648722782084681, 37648722782084737, 37648722782084749, 37648722782084783, 37648722782084807, 37648722782084863, 37648722782084879] "list of corresponding d's=", [78, 86, 114, 126, 138, 194, 206, 240, 264, 320, 336], "delta=", 240 "factors of G(p_k,nprime)=", [1, 2], [55560252023842147, 55560252023842171], [-2], [55560252023842091, 37648722782084629] 3086941604952856725096584545781137 ----------------------------------, "ecart=", 7, "type=", 3 2091772526148387347170742894319239 "*** n=2^", 106, "p_k=", 78935883898354877, "nprime=", 28686274256363761, "***" "[number of q's, compdelta, compqmax]=", [3, 2, 1] "list of trialed q's=", [50249609641991203, 50249609641991237, 50249609641991261] "list of corresponding d's=", [44, 78, 102], "delta=", 78 "factors of G(p_k,nprime)=", [2], [78935883898354957], [], [50249609641991203] 78935883898354957 -----------------, "ecart=", 7, "type=", 3 50249609641991203 "*** n=2^", 107, "p_k=", 112141493087954879, "nprime=", 57107815856427089, "***" "[number of q's, compdelta, compqmax]=", [1, 1, 1] "list of trialed q's=", [55033677231527873] "list of corresponding d's=", [68], "delta=", 68 "factors of G(p_k,nprime)=", [1, 3], [112141493087954893, 112141493087954947], [0], [112141493087954879, 55033677231527873] 12575714471995841098727187952205671 -----------------------------------, "ecart=", 1, "type=", 3 6171558734864122771158478054842367 "*** n=2^", 108, "p_k=", 159308929519397491, "nprime=", 75642919247661640, "***" new value of maxd=, 1000 "[number of q's, compdelta, compqmax]=", [14, 8, 1] "list of trialed q's=", [83666010271736033, 83666010271736119, 83666010271736131, 83666010271736201, 83666010271736231, 83666010271736239, 83666010271736467, 83666010271736513, 83666010271736527, 83666010271736561, 83666010271736591, 83666010271736611, 83666010271736623, 83666010271736657] "list of corresponding d's=", [32, 118, 130, 200, 230, 238, 466, 512, 526, 560, 590, 610, 622, 656], "delta=", 512 "factors of G(p_k,nprime)=", [1], [159308929519397641], [], [83666010271736033] 159308929519397641 ------------------, "ecart=", 32, "type=", 3 83666010271736033 "*** n=2^", 109, "p_k=", 226306049041980031, "nprime=", 174406070796167550, "***" "[number of q's, compdelta, compqmax]=", [3, 3, 1] "list of trialed q's=", [51899978245812569, 51899978245812583, 51899978245812649] "list of corresponding d's=", [12, 26, 92], "delta=", 92 "factors of G(p_k,nprime)=", [1], [226306049041980107], [], [51899978245812569] 226306049041980107 ------------------, "ecart=", 12, "type=", 3 51899978245812569 "*** n=2^", 110, "p_k=", 321465805729626037, "nprime=", 102284797271067708, "***" "[number of q's, compdelta, compqmax]=", [8, 7, 1] "list of trialed q's=", [219181008458558413, 219181008458558441, 219181008458558449, 219181008458558453, 219181008458558459, 219181008458558467, 219181008458558521, 219181008458558527] "list of corresponding d's=", [42, 70, 78, 82, 88, 96, 150, 156], "delta=", 150 "factors of G(p_k,nprime)=", [2], [321465805729626109], [], [219181008458558413] 321465805729626109 ------------------, "ecart=", 12, "type=", 3 219181008458558413 "*** n=2^", 111, "p_k=", 456621435656355677, "nprime=", 154368688220482762, "***" "[number of q's, compdelta, compqmax]=", [1, 1, 1] "list of trialed q's=", [302252747435872951] "list of corresponding d's=", [24], "delta=", 24 "factors of G(p_k,nprime)=", [1, 2], [456621435656355689, 456621435656355701], [0], [456621435656355677, 302252747435872951] 208503135500871384073447448358932989 ------------------------------------, "ecart=", 0, "type=", 3 138015083465246184031687089839592827 "*** n=2^", 112, "p_k=", 648576188739732977, "nprime=", 541008846215755201, "***" "[number of q's, compdelta, compqmax]=", [7, 7, 1] "list of trialed q's=", [107567342523977857, 107567342523977939, 107567342523977983, 107567342523978067, 107567342523978083, 107567342523978091, 107567342523978133] "list of corresponding d's=", [14, 96, 140, 224, 240, 248, 290], "delta=", 290 "factors of G(p_k,nprime)=", [1], [648576188739733043], [], [107567342523977857] 648576188739733043 ------------------, "ecart=", 15, "type=", 3 107567342523977857 "*** n=2^", 113, "p_k=", 921189957002831419, "nprime=", 537657706675359459, "***" "[number of q's, compdelta, compqmax]=", [6, 6, 1] "list of trialed q's=", [383532250327472027, 383532250327472039, 383532250327472101, 383532250327472111, 383532250327472159, 383532250327472173] "list of corresponding d's=", [38, 50, 112, 122, 170, 184], "delta=", 184 "factors of G(p_k,nprime)=", [2], [921189957002831459], [], [383532250327472027] 921189957002831459 ------------------, "ecart=", 27, "type=", 3 383532250327472027 "*** n=2^", 114, "p_k=", 1308341646613338367, "nprime=", 353615181767568420, "***" "[number of q's, compdelta, compqmax]=", [4, 4, 1] "list of trialed q's=", [954726464845770017, 954726464845770121, 954726464845770139, 954726464845770203] "list of corresponding d's=", [24, 128, 146, 210], "delta=", 210 "factors of G(p_k,nprime)=", [2], [1308341646613338419], [], [954726464845770017] 1308341646613338419 -------------------, "ecart=", 18, "type=", 3 954726464845770017 "*** n=2^", 115, "p_k=", 1858134705721126627, "nprime=", 1392019486205659815, "***" "[number of q's, compdelta, compqmax]=", [9, 7, 1] "list of trialed q's=", [466115219515466903, 466115219515466993, 466115219515467023, 466115219515467091, 466115219515467209, 466115219515467217, 466115219515467271, 466115219515467281, 466115219515467293] "list of corresponding d's=", [20, 110, 140, 208, 326, 334, 388, 398, 410], "delta=", 388 "factors of G(p_k,nprime)=", [1], [1858134705721126697], [], [466115219515466903] 1858134705721126697 -------------------, "ecart=", 21, "type=", 3 466115219515466903 "*** n=2^", 116, "p_k=", 2638867319610280727, "nprime=", 1164786857674569691, "***" "[number of q's, compdelta, compqmax]=", [2, 1, 1] "list of trialed q's=", [1474080461935711141, 1474080461935711177] "list of corresponding d's=", [102, 138], "delta=", 102 "factors of G(p_k,nprime)=", [1, 2, 3], [2638867319610280729, 2638867319610280747, 2638867319610280769], [0, -1], [2638867319610280727, 2638867319610280687, 1474080461935711141] 18376071171895981783261589118608278879994408671978728947 --------------------------------------------------------, "ecart=", 1, 10264937263171070084156411985624108103579151002478381309 "type=", 3 "*** n=2^", 117, "p_k=", 3747507505182025829, "nprime=", 631716657140780641, "***" "[number of q's, compdelta, compqmax]=", [6, 3, 2] "list of trialed q's=", [3115790848041245399, 3115790848041245411, 3115790848041245513, 3115790848041245519, 3115790848041245557, 3115790848041245573] "list of corresponding d's=", [78, 90, 192, 198, 236, 252], "delta=", 192 "factors of G(p_k,nprime)=", [4], [3747507505182026041], [], [3115790848041245411] 3747507505182026041 -------------------, "ecart=", 11, "type=", 3 3115790848041245411 > hdedixpuisa(1,35): "*** n=10^", 1, "p_k=", 5, "nprime=", 0, "***" "nprime is smaller than p_{k+1}-p_k" "factors of G(p_k,nprime)=", [], [], [], [] 1, "ecart=", 0, "type=", 1 "*** n=10^", 2, "p_k=", 23, "nprime=", 0, "***" "nprime is smaller than p_{k+1}-p_k" "factors of G(p_k,nprime)=", [], [], [], [] 1, "ecart=", 0, "type=", 1 "*** n=10^", 3, "p_k=", 89, "nprime=", 37, "***" "mm=nprime - 1", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [97], [], [61] 97 --, "ecart=", 1, "type=", 2 61 "*** n=10^", 4, "p_k=", 331, "nprime=", 146, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [337], [], [191] 337 ---, "ecart=", 0, "type=", 2 191 "*** n=10^", 5, "p_k=", 1151, "nprime=", 315, "***" "mm=nprime - 1", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [1153], [], [839] 1153 ----, "ecart=", 1, "type=", 2 839 "*** n=10^", 6, "p_k=", 3931, "nprime=", 2339, "***" "[number of q's, compdelta, compqmax]=", [2, 2, 1] "list of trialed q's=", [1607, 1609] "list of corresponding d's=", [2, 4], "delta=", 4 "factors of G(p_k,nprime)=", [1], [3943], [], [1607] 3943 ----, "ecart=", 3, "type=", 3 1607 "*** n=10^", 7, "p_k=", 13421, "nprime=", 8555, "***" "[number of q's, compdelta, compqmax]=", [3, 2, 1] "list of trialed q's=", [4889, 4903, 4909] "list of corresponding d's=", [2, 16, 22], "delta=", 16 "factors of G(p_k,nprime)=", [1], [13441], [], [4889] 13441 -----, "ecart=", 3, "type=", 3 4889 "*** n=10^", 8, "p_k=", 45191, "nprime=", 44820, "***" "[number of q's, compdelta, compqmax]=", [7, 7, 1] "list of trialed q's=", [379, 383, 389, 397, 401, 409, 419] "list of corresponding d's=", [2, 6, 12, 20, 24, 32, 42], "delta=", 42 "factors of G(p_k,nprime)=", [1], [45197], [], [379] 45197 -----, "ecart=", 2, "type=", 3 379 "*** n=10^", 9, "p_k=", 151057, "nprime=", 133215, "***" "[number of q's, compdelta, compqmax]=", [9, 9, 1] "list of trialed q's=", [17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939] "list of corresponding d's=", [4, 14, 26, 32, 34, 44, 46, 52, 62], "delta=", 62 "factors of G(p_k,nprime)=", [1], [151091], [], [17881] 151091 ------, "ecart=", 5, "type=", 3 17881 "*** n=10^", 10, "p_k=", 502247, "nprime=", 78132, "***" "[number of q's, compdelta, compqmax]=", [1, 1, 1] "list of trialed q's=", [424129] "list of corresponding d's=", [2], "delta=", 2 "factors of G(p_k,nprime)=", [2], [502261], [], [424129] 502261 ------, "ecart=", 0, "type=", 3 424129 "*** n=10^", 11, "p_k=", 1662361, "nprime=", 679220, "***" "[number of q's, compdelta, compqmax]=", [3, 2, 1] "list of trialed q's=", [983173, 983179, 983189] "list of corresponding d's=", [16, 22, 32], "delta=", 22 "factors of G(p_k,nprime)=", [3], [1662389], [], [983173] 1662389 -------, "ecart=", 4, "type=", 3 983173 "*** n=10^", 12, "p_k=", 5477081, "nprime=", 4935150, "***" "[number of q's, compdelta, compqmax]=", [1, 1, 1] "list of trialed q's=", [541951] "list of corresponding d's=", [18], "delta=", 18 "factors of G(p_k,nprime)=", [2, 3], [5477089, 5477093], [0], [5477081, 541951] 29998525822277 --------------, "ecart=", 0, "type=", 3 2968309525031 "*** n=10^", 13, "p_k=", 17993471, "nprime=", 17687910, "***" "[number of q's, compdelta, compqmax]=", [3, 3, 1] "list of trialed q's=", [305581, 305593, 305597] "list of corresponding d's=", [14, 26, 30], "delta=", 30 "factors of G(p_k,nprime)=", [1, 2], [17993477, 17993483], [0], [17993471, 305581] 323765322510391 ---------------, "ecart=", 2, "type=", 3 5498462861651 "*** n=10^", 14, "p_k=", 58954409, "nprime=", 18206505, "***" "mm=nprime - 1", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [58954411], [], [40747907] 58954411 --------, "ecart=", 1, "type=", 2 40747907 "*** n=10^", 15, "p_k=", 192682397, "nprime=", 79297359, "***" "[number of q's, compdelta, compqmax]=", [2, 2, 2] "list of trialed q's=", [113385187, 113385191] "list of corresponding d's=", [8, 12], "delta=", 12 "factors of G(p_k,nprime)=", [4], [192682549], [], [113385191] 192682549 ---------, "ecart=", 1, "type=", 3 113385191 "*** n=10^", 16, "p_k=", 628420087, "nprime=", 468817588, "***" "[number of q's, compdelta, compqmax]=", [5, 5, 1] "list of trialed q's=", [159602561, 159602563, 159602567, 159602587, 159602593] "list of corresponding d's=", [20, 22, 26, 46, 52], "delta=", 52 "factors of G(p_k,nprime)=", [2], [628420139], [], [159602561] 628420139 ---------, "ecart=", 10, "type=", 3 159602561 "*** n=10^", 17, "p_k=", 2045812129, "nprime=", 530434512, "***" "[number of q's, compdelta, compqmax]=", [12, 8, 1] "list of trialed q's=", [1515377651, 1515377657, 1515377761, 1515377767, 1515377783, 1515377789, 1515377791, 1515377833, 1515377837, 1515377869, 1515377879, 1515377887] "list of corresponding d's=", [6, 12, 116, 122, 138, 144, 146, 188, 192, 224, 234, 242], "delta=", 188 "factors of G(p_k,nprime)=", [1], [2045812157], [], [1515377651] 2045812157 ----------, "ecart=", 6, "type=", 3 1515377651 "*** n=10^", 18, "p_k=", 6649205947, "nprime=", 4975017306, "***" "[number of q's, compdelta, compqmax]=", [4, 2, 1] "list of trialed q's=", [1674188651, 1674188687, 1674188689, 1674188693] "list of corresponding d's=", [6, 42, 44, 48], "delta=", 42 "factors of G(p_k,nprime)=", [1], [6649205951], [], [1674188651] 6649205951 ----------, "ecart=", 6, "type=", 3 1674188651 "*** n=10^", 19, "p_k=", 21579536887, "nprime=", 7802551562, "***" "mm=nprime", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [21579536893], [], [13776985331] 21579536893 -----------, "ecart=", 0, "type=", 2 13776985331 "*** n=10^", 20, "p_k=", 69943284083, "nprime=", 37512814187, "***" "[number of q's, compdelta, compqmax]=", [6, 4, 1] "list of trialed q's=", [32430469931, 32430469933, 32430469961, 32430469991, 32430469999, 32430470003] "list of corresponding d's=", [20, 22, 50, 80, 88, 92], "delta=", 80 "factors of G(p_k,nprime)=", [2], [69943284113], [], [32430469931] 69943284113 -----------, "ecart=", 5, "type=", 3 32430469931 "*** n=10^", 21, "p_k=", 226431374401, "nprime=", 142613249827, "***" "[number of q's, compdelta, compqmax]=", [6, 4, 1] "list of trialed q's=", [83818124633, 83818124639, 83818124671, 83818124681, 83818124699, 83818124701] "list of corresponding d's=", [36, 42, 74, 84, 102, 104], "delta=", 84 "factors of G(p_k,nprime)=", [3], [226431374453], [], [83818124633] 226431374453 ------------, "ecart=", 7, "type=", 3 83818124633 "*** n=10^", 22, "p_k=", 732253012133, "nprime=", 451575818329, "***" "[number of q's, compdelta, compqmax]=", [7, 7, 1] "list of trialed q's=", [280677193861, 280677193871, 280677193889, 280677193903, 280677193921, 280677193931, 280677193939] "list of corresponding d's=", [18, 28, 46, 60, 78, 88, 96], "delta=", 96 "factors of G(p_k,nprime)=", [1], [732253012171], [], [280677193861] 732253012171 ------------, "ecart=", 19, "type=", 3 280677193861 "*** n=10^", 23, "p_k=", 2365707119569, "nprime=", 2123854653548, "***" "[number of q's, compdelta, compqmax]=", [8, 8, 1] "list of trialed q's=", [241852466041, 241852466057, 241852466087, 241852466123, 241852466153, 241852466159, 241852466189, 241852466201] "list of corresponding d's=", [10, 26, 56, 92, 122, 128, 158, 170], "delta=", 170 "factors of G(p_k,nprime)=", [1], [2365707119579], [], [241852466041] 2365707119579 -------------, "ecart=", 10, "type=", 3 241852466041 "*** n=10^", 24, "p_k=", 7636102747781, "nprime=", 3265879922023, "***" "[number of q's, compdelta, compqmax]=", [5, 4, 1] "list of trialed q's=", [4370222825777, 4370222825803, 4370222825849, 4370222825851, 4370222825887] "list of corresponding d's=", [10, 36, 82, 84, 120], "delta=", 84 "factors of G(p_k,nprime)=", [1], [7636102747789], [], [4370222825777] 7636102747789 -------------, "ecart=", 11, "type=", 3 4370222825777 "*** n=10^", 25, "p_k=", 24627776204923, "nprime=", 19762898291976, "***" "[number of q's, compdelta, compqmax]=", [4, 3, 1] "list of trialed q's=", [4864877913109, 4864877913127, 4864877913143, 4864877913149] "list of corresponding d's=", [48, 66, 82, 88], "delta=", 82 "factors of G(p_k,nprime)=", [4], [24627776205083], [], [4864877913109] 24627776205083 --------------, "ecart=", 2, "type=", 3 4864877913109 "*** n=10^", 26, "p_k=", 79368662592301, "nprime=", 41809634354534, "***" "[number of q's, compdelta, compqmax]=", [5, 4, 2] "list of trialed q's=", [37559028237869, 37559028237883, 37559028237923, 37559028238073, 37559028238111] "list of corresponding d's=", [36, 50, 90, 240, 278], "delta=", 240 "factors of G(p_k,nprime)=", [3], [79368662592413], [], [37559028237883] 79368662592413 --------------, "ecart=", 4, "type=", 3 37559028237883 "*** n=10^", 27, "p_k=", 255604186937189, "nprime=", 6459083731725, "***" "[number of q's, compdelta, compqmax]=", [8, 3, 3] "list of trialed q's=", [249145103205539, 249145103205589, 249145103205629, 249145103205637, 249145103205659, 249145103205671, 249145103205703, 249145103205709] "list of corresponding d's=", [50, 100, 140, 148, 170, 182, 214, 220], "delta=", 140 "factors of G(p_k,nprime)=", [1, 5], [255604186937213, 255604186937329], [0], [255604186937189, 249145103205629] 65333500379863378911288924077 -----------------------------, "ecart=", 1, "type=", 3 63682531534256841291174236881 "*** n=10^", 28, "p_k=", 822628809813037, "nprime=", 815508130025257, "***" "mm=nprime - 1", " p_{k+1}-mm is prime" "factors of G(p_k,nprime)=", [1], [822628809813047], [], [7120679787791] 822628809813047 ---------------, "ecart=", 1, "type=", 2 7120679787791 "*** n=10^", 29, "p_k=", 2645919057430751, "nprime=", 2501502719639271, "***" "[number of q's, compdelta, compqmax]=", [8, 8, 1] "list of trialed q's=", [144416337791527, 144416337791533, 144416337791587, 144416337791597, 144416337791599, 144416337791603, 144416337791617, 144416337791639] "list of corresponding d's=", [28, 34, 88, 98, 100, 104, 118, 140], "delta=", 140 "factors of G(p_k,nprime)=", [1, 2], [2645919057430769, 2645919057430777], [0], [2645919057430751, 144416337791527] 7000887658475350229067687377513 -------------------------------, "ecart=", 3, "type=", 3 382113940366958064350077046777 "*** n=10^", 30, "p_k=", 8505572989358131, "nprime=", 7343449508390437, "***" "[number of q's, compdelta, compqmax]=", [1, 1, 1] "list of trialed q's=", [1162123480967741] "list of corresponding d's=", [10], "delta=", 10 "factors of G(p_k,nprime)=", [2], [8505572989358177], [], [1162123480967741] 8505572989358177 ----------------, "ecart=", 1, "type=", 3 1162123480967741 "*** n=10^", 31, "p_k=", 27327564443962931, "nprime=", 13877499683805723, "***" "[number of q's, compdelta, compqmax]=", [10, 5, 1] "list of trialed q's=", [13450064760157297, 13450064760157351, 13450064760157367, 13450064760157373, 13450064760157507, 13450064760157513, 13450064760157523, 13450064760157537, 13450064760157547, 13450064760157549] "list of corresponding d's=", [22, 76, 92, 98, 232, 238, 248, 262, 272, 274], "delta=", 232 "factors of G(p_k,nprime)=", [2], [27327564443963009], [], [13450064760157297] 27327564443963009 -----------------, "ecart=", 11, "type=", 3 13450064760157297 "*** n=10^", 32, "p_k=", 87757258184451287, "nprime=", 25633740738769901, "***" "[number of q's, compdelta, compqmax]=", [1, 1, 1] "list of trialed q's=", [62123517445681441] "list of corresponding d's=", [42], "delta=", 42 "factors of G(p_k,nprime)=", [1, 3], [87757258184451299, 87757258184451329], [0], [87757258184451287, 62123517445681441] 7701336364052447136296311236326371 ----------------------------------, "ecart=", 1, "type=", 3 5451789559806929949471672384464567 "*** n=10^", 33, "p_k=", 281684563123416169, "nprime=", 227862450865627006, "***" "[number of q's, compdelta, compqmax]=", [7, 5, 1] "list of trialed q's=", [53822112257789257, 53822112257789263, 53822112257789279, 53822112257789329, 53822112257789471, 53822112257789479, 53822112257789489] "list of corresponding d's=", [16, 22, 38, 88, 230, 238, 248], "delta=", 230 "factors of G(p_k,nprime)=", [2], [281684563123416259], [], [53822112257789257] 281684563123416259 ------------------, "ecart=", 4, "type=", 3 53822112257789257 "*** n=10^", 34, "p_k=", 903759496776593377, "nprime=", 679498720026090893, "***" "[number of q's, compdelta, compqmax]=", [5, 5, 1] "list of trialed q's=", [224260776750502553, 224260776750502561, 224260776750502601, 224260776750502627, 224260776750502651] "list of corresponding d's=", [22, 30, 70, 96, 120], "delta=", 120 "factors of G(p_k,nprime)=", [1], [903759496776593423], [], [224260776750502553] 903759496776593423 ------------------, "ecart=", 23, "type=", 3 224260776750502553 "*** n=10^", 35, "p_k=", 2898434150644708999, "nprime=", 1886081812111845520, "***" "[number of q's, compdelta, compqmax]=", [5, 3, 1] "list of trialed q's=", [1012352338532863519, 1012352338532863553, 1012352338532863637, 1012352338532863649, 1012352338532863663] "list of corresponding d's=", [16, 50, 134, 146, 160], "delta=", 134 "factors of G(p_k,nprime)=", [1], [2898434150644709023], [], [1012352338532863519] 2898434150644709023 -------------------, "ecart=", 16, "type=", 3 1012352338532863519