# Tables of Quartics unramified outside S

## Cases where S contains one prime

 S S4 A4 D4 C4 V Total {2} 4 2 1 7 txt gp {3} 0 {5} 1 1 txt gp {7} 0 {11} 0 {13} 1 1 txt gp {17} 1 1 txt gp {19} 0 {23} 0 {29} 1 1 txt gp {31} 0 {37} 1 1 txt gp {41} 1 1 txt gp {43} 0 {47} 0 {53} 1 1 txt gp {59} 1 1 txt gp {61} 1 1 txt gp {67} 0 {71} 0 {73} 1 1 txt gp {79} 0 {83} 0 {89} 1 1 txt gp {97} 1 1 txt gp {101} 1 1 txt gp {103} 0 {107} 1 1 txt gp {109} 1 1 txt gp {113} 1 1 txt gp {127} 0 {131} 0 {137} 1 1 txt gp {139} 1 1 txt gp {149} 1 1 txt gp {151} 0 {157} 1 1 txt gp {163} 1 1 txt gp {167} 0 {173} 1 1 txt gp {179} 0 {181} 1 1 txt gp {191} 0 {193} 1 1 txt gp {197} 1 1 txt gp {199} 0 {211} 0 {223} 0 {227} 0 {229} 3 1 4 txt gp

## Cases where S contains two primes

 S S4 A4 D4 C4 V Total {2,3} 22 1 28 4 7 62 txt gp {2,5} 3 24 12 7 46 txt gp {3,5} 1 2 1 4 txt gp {2,7} 1 40 4 7 52 txt gp {3,7} 1 2 1 4 txt gp {5,7} 2 1 3 txt gp {2,11} 6 28 4 7 45 txt gp {3,11} 3 2 1 6 txt gp {5,11} 4 2 1 7 txt gp {7,11} 2 1 3 txt gp {2,13} 10 1 24 12 7 54 txt gp {3,13} 1 4 2 1 8 txt gp {5,13} 1 6 1 8 txt gp {7,13} 1 2 1 4 txt gp {11,13} 1 2 1 4 txt gp {2,17} 60 12 7 79 txt gp {3,17} 2 1 2 1 6 txt gp {5,17} 6 1 7 txt gp {7,17} 2 1 3 txt gp {11,17} 1 2 1 4 txt gp {13,17} 6 6 1 13 txt gp {2,19} 13 1 28 4 7 53 txt gp {3,19} 2 1 2 1 6 txt gp {5,19} 4 2 1 7 txt gp {7,19} 1 2 1 4 txt gp {11,19} 1 2 1 4 txt gp {13,19} 1 2 1 4 txt gp {17,19} 4 2 1 7 txt gp {2,23} 9 40 4 7 60 txt gp {3,23} 3 2 1 6 txt gp {5,23} 1 2 1 4 txt gp {7,23} 1 2 1 4 txt gp {11,23} 1 2 1 4 txt gp {13,23} 4 2 1 7 txt gp {17,23} 1 2 1 4 txt gp {19,23} 1 2 1 4 txt gp {2,29} 17 24 12 7 60 txt gp {3,29} 4 2 1 7 txt gp {5,29} 6 6 1 13 txt gp {7,29} 1 4 2 1 8 txt gp {11,29} 1 2 1 4 txt gp {13,29} 6 6 1 13 txt gp {17,29} 6 1 7 txt gp {19,29} 1 2 1 4 txt gp {23,29} 4 2 1 7 txt gp {2,31} 3 5 40 4 7 59 txt gp {3,31} 2 2 1 5 txt gp {5,31} 4 2 1 7 txt gp {7,31} 2 1 3 txt gp {11,31} 2 2 1 5 txt gp {13,31} 1 1 2 1 5 txt gp {17,31} 2 2 1 5 txt gp {19,31} 1 2 1 4 txt gp {23,31} 1 1 2 1 5 txt gp {29,31} 1 1 2 1 5 txt gp {2,37} 10 1 24 12 7 54 txt gp {3,37} 1 1 4 2 1 9 txt gp {5,37} 6 1 7 txt gp {7,37} 4 2 1 7 txt gp {11,37} 1 4 2 1 8 txt gp {13,37} 6 1 7 txt gp {17,37} 6 1 7 txt gp {19,37} 2 2 1 5 txt gp {23,37} 1 1 2 1 5 txt gp {29,37} 1 6 1 8 txt gp {31,37} 4 2 2 1 9 txt gp {2,41} 60 12 7 79 txt gp {3,41} 5 2 1 8 txt gp {5,41} 6 6 1 13 txt gp {7,41} 1 2 1 4 txt gp {11,41} 3 2 1 6 txt gp {13,41} 1 6 1 8 txt gp {17,41} 4 6 1 11 txt gp {19,41} 3 2 1 6 txt gp {23,41} 4 2 1 7 txt gp {29,41} 1 6 1 8 txt gp {31,41} 4 2 1 7 txt gp {37,41} 6 6 1 13 txt gp {2,43} 6 5 28 4 7 50 txt gp {3,43} 3 2 1 6 txt gp {5,43} 1 2 1 4 txt gp {7,43} 1 2 1 4 txt gp {11,43} 3 1 2 1 7 txt gp {13,43} 1 4 2 1 8 txt gp {17,43} 3 4 2 1 10 txt gp {19,43} 2 1 3 txt gp {23,43} 1 2 1 4 txt gp {29,43} 2 1 3 txt gp {31,43} 1 1 2 1 5 txt gp {37,43} 1 2 1 4 txt gp {41,43} 1 1 4 2 1 9 txt gp {2,47} 6 40 4 7 57 txt gp {3,47} 5 2 1 8 txt gp {5,47} 3 2 1 6 txt gp {7,47} 1 2 1 4 txt gp {11,47} 2 1 3 txt gp {13,47} 1 2 1 4 txt gp {17,47} 4 2 1 7 txt gp {19,47} 2 1 3 txt gp {23,47} 2 1 3 txt gp {29,47} 2 2 1 5 txt gp {31,47} 3 1 2 1 7 txt gp {37,47} 1 4 2 1 8 txt gp {41,47} 1 2 1 4 txt gp {43,47} 3 1 2 1 7 txt gp {2,53} 21 24 12 7 64 txt gp {3,53} 1 1 2 1 5 txt gp {5,53} 6 1 7 txt gp {7,53} 3 4 2 1 10 txt gp {11,53} 4 2 1 7 txt gp {13,53} 1 6 6 1 14 txt gp {17,53} 6 6 1 13 txt gp {19,53} 1 2 1 4 txt gp {23,53} 5 2 1 8 txt gp {29,53} 6 6 1 13 txt gp {31,53} 1 2 1 4 txt gp {37,53} 6 6 1 13 txt gp {41,53} 6 1 7 txt gp {43,53} 3 4 2 1 10 txt gp {47,53} 1 4 2 1 8 txt gp {2,59} 24 28 4 7 63 txt gp {3,59} 2 2 1 5 txt gp {5,59} 1 4 2 1 8 txt gp {7,59} 2 2 1 5 txt gp {11,59} 1 2 1 4 txt gp {13,59} 1 2 1 4 txt gp {17,59} 3 4 2 1 10 txt gp {19,59} 2 2 1 5 txt gp {23,59} 4 2 1 7 txt gp {29,59} 1 4 2 1 8 txt gp {31,59} 3 2 1 6 txt gp {37,59} 4 2 1 7 txt gp {41,59} 1 4 2 1 8 txt gp {43,59} 3 1 2 1 7 txt gp {47,59} 1 2 1 4 txt gp {53,59} 2 4 2 1 9 txt gp {2,61} 10 1 24 12 7 54 txt gp {3,61} 2 1 4 2 1 10 txt gp {5,61} 6 6 1 13 txt gp {7,61} 2 1 3 txt gp {11,61} 1 1 2 1 5 txt gp {13,61} 3 6 6 1 16 txt gp {17,61} 6 1 7 txt gp {19,61} 1 4 2 1 8 txt gp {23,61} 2 1 2 1 6 txt gp {29,61} 6 1 7 txt gp {31,61} 1 1 2 1 5 txt gp {37,61} 1 6 1 8 txt gp {41,61} 1 6 6 1 14 txt gp {43,61} 2 1 3 txt gp {47,61} 4 4 2 1 11 txt gp {53,61} 3 1 6 1 11 txt gp {59,61} 2 2 1 5 txt gp {2,67} 6 1 28 4 7 46 txt gp {3,67} 6 1 2 1 10 txt gp {5,67} 2 1 2 1 6 txt gp {7,67} 3 2 1 6 txt gp {11,67} 1 2 1 4 txt gp {13,67} 2 1 3 txt gp {17,67} 4 2 1 7 txt gp {19,67} 1 2 1 4 txt gp {23,67} 1 2 1 4 txt gp {29,67} 4 2 1 7 txt gp {31,67} 3 1 2 1 7 txt gp {37,67} 4 4 2 1 11 txt gp {41,67} 2 2 1 5 txt gp {43,67} 3 2 2 1 8 txt gp {47,67} 2 1 3 txt gp {53,67} 3 1 2 1 7 txt gp {59,67} 1 1 2 1 5 txt gp {61,67} 1 2 1 4 txt gp {2,71} 25 40 4 7 76 txt gp {3,71} 3 1 2 1 7 txt gp {5,71} 4 2 1 7 txt gp {7,71} 1 2 1 4 txt gp {11,71} 1 2 1 4 txt gp {13,71} 2 1 3 txt gp {17,71} 1 2 1 4 txt gp {19,71} 1 2 1 4 txt gp {23,71} 1 2 1 4 txt gp {29,71} 4 2 1 7 txt gp {31,71} 2 1 3 txt gp {37,71} 1 4 2 1 8 txt gp {41,71} 2 2 1 5 txt gp {43,71} 2 2 1 5 txt gp {47,71} 1 2 1 4 txt gp {53,71} 4 2 1 7 txt gp {59,71} 3 2 1 6 txt gp {61,71} 1 2 1 4 txt gp {67,71} 2 1 3 txt gp {2,73} 6 1 60 12 7 86 txt gp {3,73} 6 2 4 2 1 15 txt gp {5,73} 1 6 1 8 txt gp {7,73} 1 2 1 4 txt gp {11,73} 2 1 3 txt gp {13,73} 2 6 1 9 txt gp {17,73} 1 6 1 8 txt gp {19,73} 4 2 1 7 txt gp {23,73} 4 2 1 7 txt gp {29,73} 6 1 7 txt gp {31,73} 1 2 1 4 txt gp {37,73} 3 1 6 6 1 17 txt gp {41,73} 3 6 6 1 16 txt gp {43,73} 1 2 1 4 txt gp {47,73} 3 2 1 6 txt gp {53,73} 6 1 7 txt gp {59,73} 4 2 1 7 txt gp {61,73} 6 6 1 13 txt gp {67,73} 4 2 1 7 txt gp {71,73} 4 2 1 7 txt gp {2,79} 22 1 40 4 7 74 txt gp {3,79} 2 1 2 1 6 txt gp {5,79} 4 2 1 7 txt gp {7,79} 1 2 1 4 txt gp {11,79} 2 1 3 txt gp {13,79} 1 1 4 2 1 9 txt gp {17,79} 1 2 1 4 txt gp {19,79} 2 1 3 txt gp {23,79} 1 2 1 4 txt gp {29,79} 2 2 1 5 txt gp {31,79} 1 2 1 4 txt gp {37,79} 1 2 1 4 txt gp {41,79} 1 1 2 1 5 txt gp {43,79} 1 2 1 4 txt gp {47,79} 2 1 3 txt gp {53,79} 1 2 1 4 txt gp {59,79} 1 2 1 4 txt gp {61,79} 1 2 2 1 6 txt gp {67,79} 1 1 2 1 5 txt gp {71,79} 1 2 1 4 txt gp {73,79} 2 1 4 2 1 10 txt gp {2,83} 10 28 4 7 49 txt gp {3,83} 4 2 1 7 txt gp {5,83} 4 2 1 7 txt gp {7,83} 1 2 1 4 txt gp {11,83} 1 2 1 4 txt gp {13,83} 1 1 2 1 5 txt gp {17,83} 4 2 1 7 txt gp {19,83} 1 1 2 1 5 txt gp {23,83} 4 2 1 7 txt gp {29,83} 4 2 1 7 txt gp {31,83} 1 2 1 4 txt gp {37,83} 4 2 1 7 txt gp {41,83} 3 4 2 1 10 txt gp {43,83} 4 2 1 7 txt gp {47,83} 1 2 1 4 txt gp {53,83} 2 2 1 5 txt gp {59,83} 1 2 1 4 txt gp {61,83} 6 4 2 1 13 txt gp {67,83} 1 2 1 4 txt gp {71,83} 1 2 1 4 txt gp {73,83} 1 1 2 1 5 txt gp {79,83} 4 2 1 7 txt gp {2,89} 7 60 12 7 86 txt gp {3,89} 2 1 2 1 6 txt gp {5,89} 6 6 1 13 txt gp {7,89} 2 1 3 txt gp {11,89} 4 2 1 7 txt gp {13,89} 6 1 7 txt gp {17,89} 6 6 1 13 txt gp {19,89} 4 2 1 7 txt gp {23,89} 2 2 1 5 txt gp {29,89} 3 6 1 10 txt gp {31,89} 2 1 2 1 6 txt gp {37,89} 1 6 1 8 txt gp {41,89} 6 1 7 txt gp {43,89} 2 1 3 txt gp {47,89} 4 2 1 7 txt gp {53,89} 6 6 1 13 txt gp {59,89} 1 2 1 4 txt gp {61,89} 3 1 6 1 11 txt gp {67,89} 3 1 4 2 1 11 txt gp {71,89} 4 2 1 7 txt gp {73,89} 6 6 1 13 txt gp {79,89} 1 1 4 2 1 9 txt gp {83,89} 4 2 1 7 txt gp {2,97} 6 1 60 12 7 86 txt gp {3,97} 9 4 2 1 16 txt gp {5,97} 6 1 7 txt gp {7,97} 1 2 2 1 6 txt gp {11,97} 2 4 2 1 9 txt gp {13,97} 6 1 7 txt gp {17,97} 6 1 7 txt gp {19,97} 1 1 2 1 5 txt gp {23,97} 2 2 1 5 txt gp {29,97} 1 6 1 8 txt gp {31,97} 1 1 4 2 1 9 txt gp {37,97} 1 6 1 8 txt gp {41,97} 6 1 7 txt gp {43,97} 3 1 4 2 1 11 txt gp {47,97} 2 1 4 2 1 10 txt gp {53,97} 6 6 1 13 txt gp {59,97} 6 2 1 9 txt gp {61,97} 6 6 1 13 txt gp {67,97} 1 2 1 4 txt gp {71,97} 1 2 1 4 txt gp {73,97} 1 6 6 1 14 txt gp {79,97} 2 4 2 1 9 txt gp {83,97} 1 2 1 4 txt gp {89,97} 1 6 6 1 14 txt gp {2,101} 21 24 12 7 64 txt gp {3,101} 4 2 1 7 txt gp {5,101} 6 6 1 13 txt gp {7,101} 1 2 1 4 txt gp {11,101} 1 2 1 4 txt gp {13,101} 6 6 1 13 txt gp {17,101} 6 6 1 13 txt gp {19,101} 4 2 1 7 txt gp {23,101} 3 4 2 1 10 txt gp {29,101} 6 1 7 txt gp {31,101} 1 4 2 1 8 txt gp {37,101} 1 6 6 1 14 txt gp {41,101} 6 1 7 txt gp {43,101} 3 4 2 1 10 txt gp {47,101} 4 2 1 7 txt gp {53,101} 3 6 1 10 txt gp {59,101} 4 2 1 7 txt gp {61,101} 3 6 1 10 txt gp {67,101} 3 2 1 6 txt gp {71,101} 4 2 1 7 txt gp {73,101} 3 6 1 10 txt gp {79,101} 1 4 2 1 8 txt gp {83,101} 1 2 1 4 txt gp {89,101} 1 6 1 8 txt gp {97,101} 1 6 6 1 14 txt gp {2,103} 7 1 40 4 7 59 txt gp {3,103} 2 1 2 1 6 txt gp {5,103} 3 2 1 6 txt gp {7,103} 2 1 3 txt gp {11,103} 1 2 1 4 txt gp {13,103} 2 4 2 1 9 txt gp {17,103} 1 4 2 1 8 txt gp {19,103} 4 2 2 1 9 txt gp {23,103} 1 1 2 1 5 txt gp {29,103} 1 4 2 1 8 txt gp {31,103} 2 2 1 5 txt gp {37,103} 2 2 1 5 txt gp {41,103} 4 2 1 7 txt gp {43,103} 1 2 1 4 txt gp {47,103} 4 2 1 7 txt gp {53,103} 2 1 3 txt gp {59,103} 1 2 1 4 txt gp {61,103} 4 2 4 2 1 13 txt gp {67,103} 6 2 1 9 txt gp {71,103} 2 2 1 5 txt gp {73,103} 3 2 1 6 txt gp {79,103} 1 2 1 4 txt gp {83,103} 1 2 1 4 txt gp {89,103} 1 1 2 1 5 txt gp {97,103} 4 2 1 7 txt gp {101,103} 3 2 1 6 txt gp {2,107} 21 28 4 7 60 txt gp {3,107} 6 1 2 1 10 txt gp {5,107} 2 2 1 5 txt gp {7,107} 3 2 1 6 txt gp {11,107} 1 2 1 4 txt gp {13,107} 1 4 2 1 8 txt gp {17,107} 1 2 1 4 txt gp {19,107} 2 1 2 1 6 txt gp {23,107} 2 2 1 5 txt gp {29,107} 3 4 2 1 10 txt gp {31,107} 1 2 1 4 txt gp {37,107} 1 4 2 1 8 txt gp {41,107} 1 4 2 1 8 txt gp {43,107} 3 1 2 1 7 txt gp {47,107} 4 2 1 7 txt gp {53,107} 1 4 2 1 8 txt gp {59,107} 7 2 1 10 txt gp {61,107} 1 4 2 1 8 txt gp {67,107} 1 1 2 1 5 txt gp {71,107} 1 2 1 4 txt gp {73,107} 5 2 1 8 txt gp {79,107} 3 2 1 6 txt gp {83,107} 4 2 1 7 txt gp {89,107} 4 4 2 1 11 txt gp {97,107} 2 2 1 5 txt gp {101,107} 2 4 2 1 9 txt gp {103,107} 1 2 1 4 txt gp {2,109} 10 5 24 12 7 58 txt gp {3,109} 4 1 4 2 1 12 txt gp {5,109} 6 6 1 13 txt gp {7,109} 1 4 2 1 8 txt gp {11,109} 3 2 1 6 txt gp {13,109} 1 6 1 8 txt gp {17,109} 1 6 1 8 txt gp {19,109} 1 1 2 1 5 txt gp {23,109} 1 1 2 1 5 txt gp {29,109} 6 6 1 13 txt gp {31,109} 1 4 2 1 8 txt gp {37,109} 6 1 7 txt gp {41,109} 1 6 1 8 txt gp {43,109} 1 1 4 2 1 9 txt gp {47,109} 2 1 3 txt gp {53,109} 1 6 1 8 txt gp {59,109} 4 2 1 7 txt gp {61,109} 6 6 1 13 txt gp {67,109} 1 1 2 1 5 txt gp {71,109} 1 4 2 1 8 txt gp {73,109} 1 6 6 1 14 txt gp {79,109} 2 1 3 txt gp {83,109} 4 2 1 7 txt gp {89,109} 6 6 1 13 txt gp {97,109} 1 6 6 1 14 txt gp {101,109} 3 1 6 1 11 txt gp {103,109} 2 1 3 txt gp {107,109} 1 1 2 1 5 txt gp {2,113} 60 12 7 79 txt gp {3,113} 5 2 1 8 txt gp {5,113} 1 6 1 8 txt gp {7,113} 1 4 2 1 8 txt gp {11,113} 4 2 1 7 txt gp {13,113} 6 6 1 13 txt gp {17,113} 1 6 1 8 txt gp {19,113} 1 1 2 1 5 txt gp {23,113} 2 2 1 5 txt gp {29,113} 1 6 1 8 txt gp {31,113} 4 2 1 7 txt gp {37,113} 6 1 7 txt gp {41,113} 6 6 1 13 txt gp {43,113} 3 1 2 1 7 txt gp {47,113} 1 2 1 4 txt gp {53,113} 6 6 1 13 txt gp {59,113} 3 2 1 6 txt gp {61,113} 1 6 6 1 14 txt gp {67,113} 2 2 1 5 txt gp {71,113} 1 2 1 4 txt gp {73,113} 1 6 1 8 txt gp {79,113} 2 1 3 txt gp {83,113} 1 4 2 1 8 txt gp {89,113} 1 6 1 8 txt gp {97,113} 1 6 6 1 14 txt gp {101,113} 6 1 7 txt gp {103,113} 3 1 2 1 7 txt gp {107,113} 3 2 1 6 txt gp {109,113} 3 1 6 6 1 17 txt gp {2,127} 15 5 40 4 7 71 txt gp {3,127} 4 2 2 1 9 txt gp {5,127} 1 1 2 1 5 txt gp {7,127} 1 2 1 4 txt gp {11,127} 2 1 3 txt gp {13,127} 4 2 1 7 txt gp {17,127} 2 4 2 1 9 txt gp {19,127} 1 2 1 4 txt gp {23,127} 2 1 3 txt gp {29,127} 2 1 3 txt gp {31,127} 1 1 2 1 5 txt gp {37,127} 1 1 4 2 1 9 txt gp {41,127} 4 2 1 7 txt gp {43,127} 1 1 2 1 5 txt gp {47,127} 1 2 1 4 txt gp {53,127} 1 2 1 4 txt gp {59,127} 1 2 1 4 txt gp {61,127} 1 1 4 2 1 9 txt gp {67,127} 1 2 1 4 txt gp {71,127} 2 1 3 txt gp {73,127} 1 1 4 2 1 9 txt gp {79,127} 2 1 3 txt gp {83,127} 2 1 3 txt gp {89,127} 1 2 1 4 txt gp {97,127} 1 1 2 1 5 txt gp {101,127} 1 2 1 4 txt gp {103,127} 1 2 1 4 txt gp {107,127} 4 1 2 1 8 txt gp {109,127} 2 1 3 txt gp {113,127} 2 4 2 1 9 txt gp {2,131} 13 28 4 7 52 txt gp {3,131} 4 2 1 7 txt gp {5,131} 1 4 2 1 8 txt gp {7,131} 1 2 1 4 txt gp {11,131} 3 2 1 6 txt gp {13,131} 1 4 2 1 8 txt gp {17,131} 3 2 1 6 txt gp {19,131} 2 1 3 txt gp {23,131} 1 2 1 4 txt gp {29,131} 2 1 3 txt gp {31,131} 3 2 1 6 txt gp {37,131} 3 2 1 6 txt gp {41,131} 3 4 2 1 10 txt gp {43,131} 1 1 2 1 5 txt gp {47,131} 1 2 1 4 txt gp {53,131} 1 4 2 1 8 txt gp {59,131} 2 2 1 5 txt gp {61,131} 1 4 2 1 8 txt gp {67,131} 1 2 1 4 txt gp {71,131} 8 2 1 11 txt gp {73,131} 3 2 1 6 txt gp {79,131} 1 2 1 4 txt gp {83,131} 3 2 1 6 txt gp {89,131} 4 2 1 7 txt gp {97,131} 1 2 1 4 txt gp {101,131} 1 4 2 1 8 txt gp {103,131} 2 1 3 txt gp {107,131} 3 2 1 6 txt gp {109,131} 2 4 2 1 9 txt gp {113,131} 4 2 1 7 txt gp {127,131} 1 2 1 4 txt gp {2,137} 7 60 12 7 86 txt gp {3,137} 4 2 1 7 txt gp {5,137} 6 1 7 txt gp {7,137} 1 4 2 1 8 txt gp {11,137} 4 2 1 7 txt gp {13,137} 3 6 1 10 txt gp {17,137} 6 6 1 13 txt gp {19,137} 4 2 1 7 txt gp {23,137} 1 2 1 4 txt gp {29,137} 4 6 1 11 txt gp {31,137} 3 2 1 6 txt gp {37,137} 1 6 6 1 14 txt gp {41,137} 3 6 1 10 txt gp {43,137} 1 1 2 1 5 txt gp {47,137} 2 1 3 txt gp {53,137} 1 6 1 8 txt gp {59,137} 1 4 2 1 8 txt gp {61,137} 6 6 1 13 txt gp {67,137} 1 2 1 4 txt gp {71,137} 1 2 1 4 txt gp {73,137} 1 6 6 1 14 txt gp {79,137} 1 1 2 1 5 txt gp {83,137} 2 2 1 5 txt gp {89,137} 6 1 7 txt gp {97,137} 6 1 7 txt gp {101,137} 6 6 1 13 txt gp {103,137} 1 1 4 2 1 9 txt gp {107,137} 3 4 2 1 10 txt gp {109,137} 1 6 6 1 14 txt gp {113,137} 6 1 7 txt gp {127,137} 4 1 2 1 8 txt gp {131,137} 1 2 1 4 txt gp {2,139} 14 1 28 4 7 54 txt gp {3,139} 3 2 1 6 txt gp {5,139} 3 4 2 1 10 txt gp {7,139} 1 1 2 1 5 txt gp {11,139} 1 2 1 4 txt gp {13,139} 2 4 2 1 9 txt gp {17,139} 3 2 1 6 txt gp {19,139} 3 2 1 6 txt gp {23,139} 5 1 2 1 9 txt gp {29,139} 2 4 2 1 9 txt gp {31,139} 4 1 2 1 8 txt gp {37,139} 7 1 4 2 1 15 txt gp {41,139} 6 4 2 1 13 txt gp {43,139} 4 2 1 7 txt gp {47,139} 3 2 1 6 txt gp {53,139} 1 2 1 4 txt gp {59,139} 4 1 2 1 8 txt gp {61,139} 3 2 1 6 txt gp {67,139} 1 1 2 1 5 txt gp {71,139} 4 2 1 7 txt gp {73,139} 1 2 2 1 6 txt gp {79,139} 4 1 2 1 8 txt gp {83,139} 2 2 1 5 txt gp {89,139} 1 4 2 1 8 txt gp {97,139} 1 1 2 1 5 txt gp {101,139} 6 2 1 9 txt gp {103,139} 2 1 2 1 6 txt gp {107,139} 6 2 1 9 txt gp {109,139} 1 2 1 4 txt gp {113,139} 1 4 2 1 8 txt gp {127,139} 1 2 1 4 txt gp {131,139} 1 1 2 1 5 txt gp {137,139} 2 4 2 1 9 txt gp {2,149} 10 24 12 7 53 txt gp {3,149} 2 2 1 5 txt gp {5,149} 6 6 1 13 txt gp {7,149} 4 2 1 7 txt gp {11,149} 1 2 1 4 txt gp {13,149} 3 6 1 10 txt gp {17,149} 6 6 1 13 txt gp {19,149} 1 4 2 1 8 txt gp {23,149} 3 2 1 6 txt gp {29,149} 6 6 1 13 txt gp {31,149} 4 4 2 1 11 txt gp {37,149} 1 6 6 1 14 txt gp {41,149} 1 6 1 8 txt gp {43,149} 2 1 3 txt gp {47,149} 4 2 1 7 txt gp {53,149} 6 6 1 13 txt gp {59,149} 6 2 1 9 txt gp {61,149} 1 1 6 6 1 15 txt gp {67,149} 1 1 4 2 1 9 txt gp {71,149} 2 1 3 txt gp {73,149} 3 1 6 6 1 17 txt gp {79,149} 1 2 1 4 txt gp {83,149} 2 2 1 5 txt gp {89,149} 6 1 7 txt gp {97,149} 1 6 1 8 txt gp {101,149} 1 6 1 8 txt gp {103,149} 4 2 1 7 txt gp {107,149} 2 4 2 1 9 txt gp {109,149} 6 1 7 txt gp {113,149} 6 6 1 13 txt gp {127,149} 7 4 2 1 14 txt gp {131,149} 4 2 1 7 txt gp {137,149} 8 6 1 15 txt gp {139,149} 4 1 2 1 8 txt gp {2,151} 7 1 40 4 7 59 txt gp {3,151} 2 1 2 1 6 txt gp {5,151} 2 4 2 1 9 txt gp {7,151} 2 1 3 txt gp {11,151} 2 1 3 txt gp {13,151} 3 1 2 1 7 txt gp {17,151} 4 2 1 7 txt gp {19,151} 1 2 2 1 6 txt gp {23,151} 2 2 1 5 txt gp {29,151} 1 1 4 2 1 9 txt gp {31,151} 2 2 2 1 7 txt gp {37,151} 1 4 2 1 8 txt gp {41,151} 1 2 1 4 txt gp {43,151} 1 2 1 4 txt gp {47,151} 2 1 3 txt gp {53,151} 1 2 1 4 txt gp {59,151} 6 1 2 1 10 txt gp {61,151} 1 1 2 1 5 txt gp {67,151} 1 1 2 1 5 txt gp {71,151} 5 2 1 8 txt gp {73,151} 1 1 2 1 5 txt gp {79,151} 1 2 1 4 txt gp {83,151} 1 2 1 4 txt gp {89,151} 2 2 1 5 txt gp {97,151} 3 4 2 1 10 txt gp {101,151} 1 2 1 4 txt gp {103,151} 2 1 3 txt gp {107,151} 1 1 2 1 5 txt gp {109,151} 2 1 3 txt gp {113,151} 1 2 1 4 txt gp {127,151} 2 2 1 5 txt gp {131,151} 10 1 2 1 14 txt gp {137,151} 4 2 1 7 txt gp {139,151} 1 2 1 4 txt gp {149,151} 2 2 1 5 txt gp

## Cases where S contains three primes

 S S4 A4 D4 C4 V Total {2,3,5} 143 1 176 24 35 379 txt gp {2,3,7} 150 8 184 8 35 385 txt gp {2,5,7} 38 1 176 24 35 274 txt gp {3,5,7} 11 1 12 4 7 35 txt gp {2,3,11} 171 1 208 8 35 423 txt gp {2,5,11} 45 176 24 35 280 txt gp {3,5,11} 15 16 4 7 42 txt gp {2,7,11} 43 1 232 8 35 319 txt gp {3,7,11} 17 1 12 7 37 txt gp {5,7,11} 1 16 4 7 28 txt gp {2,3,13} 150 8 176 24 35 393 txt gp {2,5,13} 38 5 184 56 35 318 txt gp {3,5,13} 12 1 8 12 7 40 txt gp {2,7,13} 50 12 176 24 35 297 txt gp {3,7,13} 13 3 16 4 7 43 txt gp {5,7,13} 2 2 8 12 7 31 txt gp {2,11,13} 75 1 176 24 35 311 txt gp {3,11,13} 20 1 16 4 7 48 txt gp {5,11,13} 5 1 8 12 7 33 txt gp {7,11,13} 5 2 12 4 7 30 txt gp {2,3,17} 185 5 200 24 35 449 txt gp {2,5,17} 46 184 56 35 321 txt gp {3,5,17} 18 1 8 12 7 46 txt gp {2,7,17} 39 1 248 24 35 347 txt gp {3,7,17} 15 1 12 4 7 39 txt gp {5,7,17} 2 8 12 7 29 txt gp {2,11,17} 51 200 24 35 310 txt gp {3,11,17} 21 1 12 4 7 45 txt gp {5,11,17} 6 8 12 7 33 txt gp {7,11,17} 11 12 4 7 34 txt gp {2,13,17} 17 1 328 56 35 437 txt gp {3,13,17} 18 1 28 12 7 66 txt gp {5,13,17} 1 1 12 28 7 49 txt gp {7,13,17} 5 2 12 12 7 38 txt gp {11,13,17} 4 12 12 7 35 txt gp {2,3,19} 166 12 208 8 35 429 txt gp {2,5,19} 48 1 176 24 35 284 txt gp {3,5,19} 18 2 16 4 7 47 txt gp {2,7,19} 37 12 184 8 35 276 txt gp {3,7,19} 17 4 24 7 52 txt gp {5,7,19} 4 2 16 4 7 33 txt gp {2,11,19} 78 5 208 8 35 334 txt gp {3,11,19} 16 2 12 7 37 txt gp {5,11,19} 1 40 4 7 52 txt gp {7,11,19} 5 24 7 36 txt gp {2,13,19} 57 8 176 24 35 300 txt gp {3,13,19} 23 3 16 4 7 53 txt gp {5,13,19} 7 1 8 12 7 35 txt gp {7,13,19} 5 3 12 4 7 31 txt gp {11,13,19} 7 1 12 4 7 31 txt gp {2,17,19} 39 1 344 24 35 443 txt gp {3,17,19} 19 5 16 4 7 51 txt gp {5,17,19} 11 24 12 7 54 txt gp {7,17,19} 4 2 16 4 7 33 txt gp {11,17,19} 3 1 16 4 7 31 txt gp {13,17,19} 2 1 28 12 7 50 txt gp {2,3,23} 185 1 232 8 35 461 txt gp {2,5,23} 59 176 24 35 294 txt gp {3,5,23} 15 12 4 7 38 txt gp {2,7,23} 21 1 304 8 35 369 txt gp {3,7,23} 20 1 12 7 40 txt gp {5,7,23} 5 12 4 7 28 txt gp {2,11,23} 76 184 8 35 303 txt gp {3,11,23} 29 24 7 60 txt gp {5,11,23} 5 16 4 7 32 txt gp {7,11,23} 3 24 7 34 txt gp {2,13,23} 59 1 224 24 35 343 txt gp {3,13,23} 26 1 40 4 7 78 txt gp {5,13,23} 5 1 8 12 7 33 txt gp {7,13,23} 2 2 16 4 7 31 txt gp {11,13,23} 2 16 4 7 29 txt gp {2,17,23} 62 248 24 35 369 txt gp {3,17,23} 20 1 12 4 7 44 txt gp {5,17,23} 10 8 12 7 37 txt gp {7,17,23} 5 12 4 7 28 txt gp {11,17,23} 9 12 4 7 32 txt gp {13,17,23} 8 28 12 7 55 txt gp {2,19,23} 128 1 184 8 35 356 txt gp {3,19,23} 17 2 12 7 38 txt gp {5,19,23} 5 16 4 7 32 txt gp {7,19,23} 6 2 24 7 39 txt gp {11,19,23} 6 1 24 7 38 txt gp {13,19,23} 5 1 16 4 7 33 txt gp {17,19,23} 7 16 4 7 34 txt gp {2,3,29} 210 1 176 24 35 446 txt gp {2,5,29} 56 184 56 35 331 txt gp {3,5,29} 24 12 12 7 55 txt gp {2,7,29} 50 5 224 24 35 338 txt gp {3,7,29} 21 1 16 4 7 49 txt gp {5,7,29} 3 1 28 12 7 51 txt gp {2,11,29} 62 176 24 35 297 txt gp {3,11,29} 20 12 4 7 43 txt gp {5,11,29} 4 28 12 7 51 txt gp {7,11,29} 12 1 16 4 7 40 txt gp {2,13,29} 54 1 184 56 35 330 txt gp {3,13,29} 30 1 28 12 7 78 txt gp {5,13,29} 1 36 28 7 72 txt gp {7,13,29} 1 5 28 12 7 53 txt gp {11,13,29} 7 12 12 7 38 txt gp {2,17,29} 73 184 56 35 348 txt gp {3,17,29} 26 1 8 12 7 54 txt gp {5,17,29} 8 12 28 7 55 txt gp {7,17,29} 11 1 8 12 7 39 txt gp {11,17,29} 12 8 12 7 39 txt gp {13,17,29} 4 36 28 7 75 txt gp {2,19,29} 97 1 176 24 35 333 txt gp {3,19,29} 25 2 12 4 7 50 txt gp {5,19,29} 2 28 12 7 49 txt gp {7,19,29} 5 2 16 4 7 34 txt gp {11,19,29} 6 1 12 4 7 30 txt gp {13,19,29} 6 1 12 12 7 38 txt gp {17,19,29} 5 8 12 7 32 txt gp {2,23,29} 69 224 24 35 352 txt gp {3,23,29} 26 16 4 7 53 txt gp {5,23,29} 2 28 12 7 49 txt gp {7,23,29} 1 1 40 4 7 53 txt gp {11,23,29} 5 16 4 7 32 txt gp {13,23,29} 3 60 12 7 82 txt gp {17,23,29} 6 8 12 7 33 txt gp {19,23,29} 7 16 4 7 34 txt gp {2,3,31} 189 8 184 8 35 424 txt gp {2,5,31} 38 5 224 24 35 326 txt gp {3,5,31} 22 1 16 4 7 50 txt gp {2,7,31} 32 8 304 8 35 387 txt gp {3,7,31} 21 3 24 7 55 txt gp {5,7,31} 1 1 16 4 7 29 txt gp {2,11,31} 59 5 184 8 35 291 txt gp {3,11,31} 33 1 24 7 65 txt gp {5,11,31} 6 40 4 7 57 txt gp {7,11,31} 11 1 12 7 31 txt gp {2,13,31} 66 12 176 24 35 313 txt gp {3,13,31} 18 3 16 4 7 48 txt gp {5,13,31} 3 5 8 12 7 35 txt gp {7,13,31} 4 3 12 4 7 30 txt gp {11,13,31} 9 2 12 4 7 34 txt gp {2,17,31} 35 5 248 24 35 347 txt gp {3,17,31} 20 1 12 4 7 44 txt gp {5,17,31} 10 8 12 7 37 txt gp {7,17,31} 7 1 12 4 7 31 txt gp {11,17,31} 18 12 4 7 41 txt gp {13,17,31} 16 2 12 12 7 49 txt gp {2,19,31} 47 12 232 8 35 334 txt gp {3,19,31} 13 3 24 7 47 txt gp {5,19,31} 2 2 40 4 7 55 txt gp {7,19,31} 4 6 24 7 41 txt gp {11,19,31} 11 5 12 7 35 txt gp {13,19,31} 5 6 12 4 7 34 txt gp {17,19,31} 15 2 16 4 7 44 txt gp {2,23,31} 53 21 304 8 35 421 txt gp {3,23,31} 33 1 24 7 65 txt gp {5,23,31} 9 1 16 4 7 37 txt gp {7,23,31} 2 1 12 7 22 txt gp {11,23,31} 7 1 24 7 39 txt gp {13,23,31} 5 2 16 4 7 34 txt gp {17,23,31} 7 1 12 4 7 31 txt gp {19,23,31} 5 2 12 7 26 txt gp {2,29,31} 88 21 176 24 35 344 txt gp {3,29,31} 26 1 12 4 7 50 txt gp {5,29,31} 2 1 28 12 7 50 txt gp {7,29,31} 7 4 16 4 7 38 txt gp {11,29,31} 9 1 12 4 7 33 txt gp {13,29,31} 6 2 12 12 7 39 txt gp {17,29,31} 17 1 8 12 7 45 txt gp {19,29,31} 11 2 12 4 7 36 txt gp {23,29,31} 5 5 16 4 7 37 txt gp {2,3,37} 179 12 176 24 35 426 txt gp {2,5,37} 69 1 184 56 35 345 txt gp {3,5,37} 16 2 8 12 7 45 txt gp {2,7,37} 24 8 224 24 35 315 txt gp {3,7,37} 20 3 40 4 7 74 txt gp {5,7,37} 5 1 8 12 7 33 txt gp {2,11,37} 65 5 176 24 35 305 txt gp {3,11,37} 26 2 40 4 7 79 txt gp {5,11,37} 4 1 24 12 7 48 txt gp {7,11,37} 1 1 40 4 7 53 txt gp {2,13,37} 53 8 184 56 35 336 txt gp {3,13,37} 25 4 24 12 7 72 txt gp {5,13,37} 3 1 12 28 7 51 txt gp {7,13,37} 4 3 8 12 7 34 txt gp {11,13,37} 8 1 8 12 7 36 txt gp {2,17,37} 69 1 184 56 35 345 txt gp {3,17,37} 19 5 8 12 7 51 txt gp {5,17,37} 1 12 28 7 48 txt gp {7,17,37} 4 1 8 12 7 32 txt gp {11,17,37} 15 1 8 12 7 43 txt gp {13,17,37} 6 1 12 28 7 54 txt gp {2,19,37} 120 16 176 24 35 371 txt gp {3,19,37} 17 9 16 4 7 53 txt gp {5,19,37} 2 2 8 12 7 31 txt gp {7,19,37} 4 7 16 4 7 38 txt gp {11,19,37} 2 8 16 4 7 37 txt gp {13,19,37} 5 4 8 12 7 36 txt gp {17,19,37} 4 3 8 12 7 34 txt gp {2,23,37} 86 5 176 24 35 326 txt gp {3,23,37} 26 2 16 4 7 55 txt gp {5,23,37} 10 1 8 12 7 38 txt gp {7,23,37} 7 1 16 4 7 35 txt gp {11,23,37} 7 5 16 4 7 39 txt gp {13,23,37} 5 1 8 12 7 33 txt gp {17,23,37} 5 1 8 12 7 33 txt gp {19,23,37} 7 3 12 4 7 33 txt gp {2,29,37} 92 5 184 56 35 372 txt gp {3,29,37} 18 2 8 12 7 47 txt gp {5,29,37} 4 1 12 28 7 52 txt gp {7,29,37} 7 4 24 12 7 54 txt gp {11,29,37} 11 5 8 12 7 43 txt gp {13,29,37} 3 1 12 28 7 51 txt gp {17,29,37} 4 1 12 28 7 52 txt gp {19,29,37} 2 3 8 12 7 32 txt gp {23,29,37} 14 5 8 12 7 46 txt gp {2,31,37} 80 16 176 24 35 331 txt gp {3,31,37} 24 3 16 4 7 54 txt gp {5,31,37} 10 3 8 12 7 40 txt gp {7,31,37} 13 4 16 4 7 44 txt gp {11,31,37} 12 6 16 4 7 45 txt gp {13,31,37} 10 7 8 12 7 44 txt gp {17,31,37} 14 3 8 12 7 44 txt gp {19,31,37} 12 9 12 4 7 44 txt gp {23,31,37} 7 8 12 4 7 38 txt gp {29,31,37} 7 8 8 12 7 42 txt gp {2,3,41} 240 1 200 24 35 500 txt gp {2,5,41} 10 328 56 35 429 txt gp {3,5,41} 21 12 12 7 52 txt gp {2,7,41} 70 5 248 24 35 382 txt gp {3,7,41} 17 1 12 4 7 41 txt gp {5,7,41} 5 1 12 12 7 37 txt gp {2,11,41} 56 200 24 35 315 txt gp {3,11,41} 26 12 4 7 49 txt gp {5,11,41} 4 28 12 7 51 txt gp {7,11,41} 8 1 12 4 7 32 txt gp {2,13,41} 91 1 184 56 35 367 txt gp {3,13,41} 20 1 8 12 7 48 txt gp {5,13,41} 3 1 12 28 7 51 txt gp {7,13,41} 5 5 8 12 7 37 txt gp {11,13,41} 20 8 12 7 47 txt gp {2,17,41} 65 328 56 35 484 txt gp {3,17,41} 28 1 8 12 7 56 txt gp {5,17,41} 9 12 28 7 56 txt gp {7,17,41} 8 1 8 12 7 36 txt gp {11,17,41} 30 8 12 7 57 txt gp {13,17,41} 12 12 28 7 59 txt gp {2,19,41} 67 1 200 24 35 327 txt gp {3,19,41} 20 2 12 4 7 45 txt gp {5,19,41} 6 28 12 7 53 txt gp {7,19,41} 12 2 12 4 7 37 txt gp {11,19,41} 19 1 12 4 7 43 txt gp {13,19,41} 20 1 8 12 7 48 txt gp {17,19,41} 15 8 12 7 42 txt gp {2,23,41} 35 440 24 35 534 txt gp {3,23,41} 33 16 4 7 60 txt gp {5,23,41} 5 28 12 7 52 txt gp {7,23,41} 9 1 16 4 7 37 txt gp {11,23,41} 7 16 4 7 34 txt gp {13,23,41} 4 24 12 7 47 txt gp {17,23,41} 17 8 12 7 44 txt gp {19,23,41} 7 16 4 7 34 txt gp {2,29,41} 93 184 56 35 368 txt gp {3,29,41} 39 8 12 7 66 txt gp {5,29,41} 4 36 28 7 75 txt gp {7,29,41} 5 5 8 12 7 37 txt gp {11,29,41} 16 8 12 7 43 txt gp {13,29,41} 2 12 28 7 49 txt gp {17,29,41} 10 12 28 7 57 txt gp {19,29,41} 12 8 12 7 39 txt gp {23,29,41} 11 24 12 7 54 txt gp {2,31,41} 3 5 440 24 35 507 txt gp {3,31,41} 29 1 16 4 7 57 txt gp {5,31,41} 3 60 12 7 82 txt gp {7,31,41} 4 1 16 4 7 32 txt gp {11,31,41} 7 16 4 7 34 txt gp {13,31,41} 8 2 8 12 7 37 txt gp {17,31,41} 12 8 12 7 39 txt gp {19,31,41} 13 2 16 4 7 42 txt gp {23,31,41} 5 1 40 4 7 57 txt gp {29,31,41} 9 1 8 12 7 37 txt gp {2,37,41} 32 1 328 56 35 452 txt gp {3,37,41} 29 2 28 12 7 78 txt gp {5,37,41} 36 28 7 71 txt gp {7,37,41} 9 1 28 12 7 57 txt gp {11,37,41} 11 1 28 12 7 59 txt gp {13,37,41} 6 1 12 28 7 54 txt gp {17,37,41} 8 12 28 7 55 txt gp {19,37,41} 11 2 12 12 7 44 txt gp {23,37,41} 8 1 28 12 7 56 txt gp {29,37,41} 7 1 12 28 7 55 txt gp {31,37,41} 8 3 28 12 7 58 txt gp

## Cases where S contains four primes

 S S4 A4 D4 C4 V Total {2,3,5,7} 894 12 1056 48 155 2165 txt gp {2,3,5,11} 955 1 1056 48 155 2215 txt gp {2,3,7,11} 998 12 1120 16 155 2301 txt gp {2,5,7,11} 277 1 1152 48 155 1633 txt gp {3,5,7,11} 110 5 96 8 35 254 txt gp {2,3,5,13} 976 12 1072 112 155 2327 txt gp {2,3,7,13} 990 41 1056 48 155 2290 txt gp {2,5,7,13} 226 16 1168 112 155 1677 txt gp {3,5,7,13} 100 7 88 24 35 254 txt gp {2,3,11,13} 1087 24 1152 48 155 2466 txt gp {2,5,11,13} 317 5 1072 112 155 1661 txt gp {3,5,11,13} 127 2 88 24 35 276 txt gp {2,7,11,13} 317 16 1152 48 155 1688 txt gp {3,7,11,13} 113 10 96 8 35 262 txt gp {5,7,11,13} 45 3 88 24 35 195 txt gp {2,3,5,17} 1023 5 1072 112 155 2367 txt gp {2,3,7,17} 1083 12 1104 48 155 2402 txt gp {2,5,7,17} 297 1 1072 112 155 1637 txt gp {3,5,7,17} 118 2 112 24 35 291 txt gp {2,3,11,17} 1143 5 1296 48 155 2647 txt gp {2,5,11,17} 359 1072 112 155 1698 txt gp {3,5,11,17} 121 1 88 24 35 269 txt gp {2,7,11,17} 388 1 1104 48 155 1696 txt gp {3,7,11,17} 116 2 96 8 35 257 txt gp {5,7,11,17} 38 88 24 35 185 txt gp {2,3,13,17} 1082 12 1168 112 155 2529 txt gp {2,5,13,17} 270 5 1200 240 155 1870 txt gp {3,5,13,17} 125 2 88 56 35 306 txt gp {2,7,13,17} 351 28 1168 112 155 1814 txt gp {3,7,13,17} 133 7 104 24 35 303 txt gp {5,7,13,17} 33 3 88 56 35 215 txt gp {2,11,13,17} 313 1 1168 112 155 1749 txt gp {3,11,13,17} 112 2 104 24 35 277 txt gp {5,11,13,17} 39 1 88 56 35 219 txt gp {7,11,13,17} 54 3 120 24 35 236 txt gp