# run2_table.py: Table 1 of the note, first R=3 weight, R=3 count (mu <= 600), large-weight probe
k=84 p=11: Case (2); chain 84>4 (R=1); w(f_k mod p)=44 (f_k mod p not in M~_34: True); admissible weights of Cor. 1.4(b): [4]; congruences for all chain members on n<3000: True; expected chain [84, 4]: True; first nonzero terms [(11, 9), (22, 4), (33, 10), (44, 8)]; 0.6s
k=84 p=17: Case (2); chain 84>4 (R=1); w(f_k mod p)=68 (f_k mod p not in M~_52: True); admissible weights of Cor. 1.4(b): [4]; congruences for all chain members on n<3000: True; expected chain [84, 4]: True; first nonzero terms [(17, 2), (34, 1), (51, 5), (68, 10)]; 0.6s
k=96 p=11: Case (2); chain 96>6 (R=1); w(f_k mod p)=66 (f_k mod p not in M~_56: True); admissible weights of Cor. 1.4(b): [6]; congruences for all chain members on n<3000: True; expected chain [96, 6]: True; first nonzero terms [(11, 2), (33, 4), (44, 2), (55, 4)]; 0.6s
k=132 p=11: Case (2); chain 132>12 (R=1); w(f_k mod p)=132 (f_k mod p not in M~_122: True); admissible weights of Cor. 1.4(b): [12]; congruences for all chain members on n<3000: True; expected chain [132, 12]: True; first nonzero terms [(22, 1), (33, 1), (44, 1), (55, 1)]; 0.6s
k=252 p=11: Case (2); chain 252>12 (R=1); w(f_k mod p)=132 (f_k mod p not in M~_122: True); admissible weights of Cor. 1.4(b): [12, 22]; congruences for all chain members on n<3000: True; expected chain [252, 12]: True; first nonzero terms [(22, 1), (33, 1), (44, 1), (55, 1)]; 0.9s
    reductions of f_w for the admissible weights [12, 22] agree on n<273: True
k=504 p=11: Case (2); chain 504>44>4 (R=2); w(f_k mod p)=484 (f_k mod p not in M~_474: True); admissible weights of Cor. 1.4(b): [44]; congruences for all chain members on n<3000: True; expected chain [504, 44, 4]: True; first nonzero terms [(121, 9), (242, 4), (363, 10), (484, 8)]; 1.1s
k=5544 p=11: Case (2); chain 5544>484>44>4 (R=3); w(f_k mod p)=5324 (f_k mod p not in M~_5314: True); admissible weights of Cor. 1.4(b): [484, 494, 504]; congruences for all chain members on n<2800: True; expected chain [5544, 484, 44, 4]: True; first nonzero terms [(1331, 9), (2662, 4)]; 7.1s
    reductions of f_w for the admissible weights [484, 494, 504] agree on n<255: True
k=5544 p=1109: Case (2); chain 5544>4 (R=1); w(f_k mod p)=4436 (f_k mod p not in M~_3328: True); admissible weights of Cor. 1.4(b): [4]; congruences for all chain members on n<3400: True; expected chain [5544, 4]: True; first nonzero terms [(1109, 240), (2218, 1051), (3327, 66)]; 10.8s
# table done 10.8s
# p=11, 444 <= mu <= 600: Case (2) for 108 weights; R >= 3 for 31 weights; first 5364 (mu=447); R values [1, 2, 3]
#   mu=444 k=5328: case 3, chain None
#   mu=445 k=5340: case 1, chain None
#   mu=446 k=5352: case 2, chain [5352, 462, 42]
#   mu=447 k=5364: case 2, chain [5364, 484, 44, 4]
# R=3 weights (mu): [447, 452, 457, 462, 467, 472, 477, 482, 487, 492, 497, 502, 507, 512, 517, 522, 527, 532, 537, 542, 547, 552, 557, 562, 567, 572, 577, 582, 587, 592, 597]
# r3 done 28.8s
# probe k=5544 (mu=462): primes 5..5545 tested; Case (2) primes: 6; outside 11 <= p <= 3mu or p = 13: []; max p = 1109; R histogram {1: 5, 3: 1}
#   (p, chain) list: [(11, '5544>484>44>4'), (31, '5544>174'), (47, '5544>116'), (59, '5544>92'), (61, '5544>84'), (1109, '5544>4')]
# probe k=7200 (mu=600): primes 5..7201 tested; Case (2) primes: 5; outside 11 <= p <= 3mu or p = 13: []; max p = 379; R histogram {1: 4, 2: 1}
#   (p, chain) list: [(29, '7200>116>4'), (89, '7200>72'), (103, '7200>60'), (277, '7200>24'), (379, '7200>18')]
# total 72.5s
