# Tables of Cubics unramified outside S

## Cases where S contains one prime

 S S3 C3 Total {2} 0 {3} 1 1 2 txt gp {5} 0 {7} 1 1 txt gp {11} 0 {13} 1 1 txt gp {17} 0 {19} 1 1 txt gp {23} 1 1 txt gp {29} 0 {31} 1 1 2 txt gp {37} 1 1 txt gp {41} 0 {43} 1 1 txt gp {47} 0 {53} 0 {59} 1 1 txt gp {61} 1 1 txt gp {67} 1 1 txt gp {71} 0 {73} 1 1 txt gp {79} 1 1 txt gp {83} 1 1 txt gp {89} 0 {97} 1 1 txt gp {101} 0 {103} 1 1 txt gp {107} 1 1 txt gp {109} 1 1 txt gp {113} 0 {127} 1 1 txt gp {131} 0 {137} 0 {139} 1 1 2 txt gp {149} 0 {151} 1 1 txt gp {157} 1 1 txt gp {163} 1 1 txt gp {167} 0 {173} 0 {179} 0 {181} 1 1 txt gp {191} 0 {193} 1 1 txt gp {197} 0 {199} 1 1 2 txt gp {211} 1 1 2 txt gp {223} 1 1 txt gp {227} 0 {229} 1 1 2 txt gp

## Cases where S contains two primes

 S S3 C3 Total {2,3} 8 1 9 txt gp {2,5} 1 1 txt gp {3,5} 5 1 6 txt gp {2,7} 1 1 txt gp {3,7} 5 4 9 txt gp {5,7} 1 1 2 txt gp {2,11} 2 2 txt gp {3,11} 6 1 7 txt gp {5,11} 0 {7,11} 1 1 txt gp {2,13} 2 1 3 txt gp {3,13} 8 4 12 txt gp {5,13} 1 1 txt gp {7,13} 4 4 txt gp {11,13} 1 1 2 txt gp {2,17} 0 {3,17} 5 1 6 txt gp {5,17} 0 {7,17} 1 1 2 txt gp {11,17} 2 2 txt gp {13,17} 1 1 txt gp {2,19} 3 1 4 txt gp {3,19} 5 4 9 txt gp {5,19} 1 1 txt gp {7,19} 1 4 5 txt gp {11,19} 1 1 txt gp {13,19} 1 4 5 txt gp {17,19} 1 1 txt gp {2,23} 3 3 txt gp {3,23} 6 1 7 txt gp {5,23} 1 1 txt gp {7,23} 1 1 2 txt gp {11,23} 1 1 txt gp {13,23} 1 1 2 txt gp {17,23} 1 1 txt gp {19,23} 1 1 2 txt gp {2,29} 3 3 txt gp {3,29} 6 1 7 txt gp {5,29} 0 {7,29} 1 1 txt gp {11,29} 1 1 txt gp {13,29} 1 1 txt gp {17,29} 0 {19,29} 1 1 2 txt gp {23,29} 1 1 txt gp {2,31} 1 1 2 txt gp {3,31} 6 4 10 txt gp {5,31} 1 1 2 txt gp {7,31} 1 4 5 txt gp {11,31} 2 1 3 txt gp {13,31} 1 4 5 txt gp {17,31} 2 1 3 txt gp {19,31} 1 4 5 txt gp {23,31} 2 1 3 txt gp {29,31} 1 1 2 txt gp {2,37} 2 1 3 txt gp {3,37} 8 4 12 txt gp {5,37} 1 1 txt gp {7,37} 1 4 5 txt gp {11,37} 1 1 2 txt gp {13,37} 4 4 txt gp {17,37} 1 1 txt gp {19,37} 4 4 txt gp {23,37} 1 1 2 txt gp {29,37} 1 1 txt gp {31,37} 2 4 6 txt gp {2,41} 0 {3,41} 5 1 6 txt gp {5,41} 0 {7,41} 1 1 2 txt gp {11,41} 2 2 txt gp {13,41} 1 1 2 txt gp {17,41} 2 2 txt gp {19,41} 1 1 2 txt gp {23,41} 1 1 txt gp {29,41} 1 1 txt gp {31,41} 1 1 2 txt gp {37,41} 1 1 txt gp {2,43} 2 1 3 txt gp {3,43} 5 4 9 txt gp {5,43} 1 1 2 txt gp {7,43} 1 4 5 txt gp {11,43} 1 1 2 txt gp {13,43} 1 4 5 txt gp {17,43} 1 1 2 txt gp {19,43} 1 4 5 txt gp {23,43} 1 1 2 txt gp {29,43} 1 1 2 txt gp {31,43} 2 4 6 txt gp {37,43} 4 4 txt gp {41,43} 1 1 2 txt gp {2,47} 2 2 txt gp {3,47} 6 1 7 txt gp {5,47} 2 2 txt gp {7,47} 2 1 3 txt gp {11,47} 1 1 txt gp {13,47} 1 1 txt gp {17,47} 0 {19,47} 1 1 txt gp {23,47} 2 2 txt gp {29,47} 2 2 txt gp {31,47} 1 1 2 txt gp {37,47} 1 1 2 txt gp {41,47} 2 2 txt gp {43,47} 1 1 2 txt gp {2,53} 3 3 txt gp {3,53} 5 1 6 txt gp {5,53} 0 {7,53} 1 1 2 txt gp {11,53} 0 {13,53} 1 1 txt gp {17,53} 0 {19,53} 2 1 3 txt gp {23,53} 3 3 txt gp {29,53} 0 {31,53} 4 1 5 txt gp {37,53} 1 1 txt gp {41,53} 0 {43,53} 1 1 2 txt gp {47,53} 1 1 txt gp {2,59} 4 4 txt gp {3,59} 6 1 7 txt gp {5,59} 1 1 txt gp {7,59} 5 1 6 txt gp {11,59} 1 1 txt gp {13,59} 1 1 2 txt gp {17,59} 1 1 txt gp {19,59} 2 1 3 txt gp {23,59} 2 2 txt gp {29,59} 1 1 txt gp {31,59} 2 1 3 txt gp {37,59} 2 1 3 txt gp {41,59} 1 1 txt gp {43,59} 1 1 2 txt gp {47,59} 1 1 txt gp {53,59} 2 2 txt gp {2,61} 2 1 3 txt gp {3,61} 8 4 12 txt gp {5,61} 1 1 txt gp {7,61} 4 4 txt gp {11,61} 1 1 2 txt gp {13,61} 1 4 5 txt gp {17,61} 1 1 txt gp {19,61} 1 4 5 txt gp {23,61} 2 1 3 txt gp {29,61} 1 1 txt gp {31,61} 1 4 5 txt gp {37,61} 4 4 txt gp {41,61} 1 1 txt gp {43,61} 4 4 txt gp {47,61} 2 1 3 txt gp {53,61} 1 1 2 txt gp {59,61} 2 1 3 txt gp {2,67} 2 1 3 txt gp {3,67} 5 4 9 txt gp {5,67} 2 1 3 txt gp {7,67} 2 4 6 txt gp {11,67} 2 1 3 txt gp {13,67} 4 4 txt gp {17,67} 1 1 txt gp {19,67} 1 4 5 txt gp {23,67} 1 1 2 txt gp {29,67} 1 1 txt gp {31,67} 1 4 5 txt gp {37,67} 2 4 6 txt gp {41,67} 2 1 3 txt gp {43,67} 1 4 5 txt gp {47,67} 1 1 txt gp {53,67} 1 1 2 txt gp {59,67} 1 1 2 txt gp {61,67} 1 4 5 txt gp {2,71} 3 3 txt gp {3,71} 6 1 7 txt gp {5,71} 0 {7,71} 1 1 txt gp {11,71} 1 1 txt gp {13,71} 1 1 txt gp {17,71} 2 2 txt gp {19,71} 2 1 3 txt gp {23,71} 2 2 txt gp {29,71} 0 {31,71} 1 1 2 txt gp {37,71} 2 1 3 txt gp {41,71} 3 3 txt gp {43,71} 2 1 3 txt gp {47,71} 1 1 txt gp {53,71} 3 3 txt gp {59,71} 2 2 txt gp {61,71} 1 1 2 txt gp {67,71} 1 1 txt gp {2,73} 2 1 3 txt gp {3,73} 8 4 12 txt gp {5,73} 1 1 2 txt gp {7,73} 4 4 txt gp {11,73} 1 1 txt gp {13,73} 4 4 txt gp {17,73} 1 1 txt gp {19,73} 1 4 5 txt gp {23,73} 1 1 2 txt gp {29,73} 1 1 txt gp {31,73} 1 4 5 txt gp {37,73} 1 4 5 txt gp {41,73} 1 1 2 txt gp {43,73} 4 4 txt gp {47,73} 1 1 2 txt gp {53,73} 1 1 txt gp {59,73} 2 1 3 txt gp {61,73} 4 4 txt gp {67,73} 1 4 5 txt gp {71,73} 1 1 2 txt gp {2,79} 2 1 3 txt gp {3,79} 5 4 9 txt gp {5,79} 1 1 txt gp {7,79} 1 4 5 txt gp {11,79} 1 1 txt gp {13,79} 2 4 6 txt gp {17,79} 1 1 2 txt gp {19,79} 1 4 5 txt gp {23,79} 1 1 2 txt gp {29,79} 2 1 3 txt gp {31,79} 2 4 6 txt gp {37,79} 1 4 5 txt gp {41,79} 1 1 2 txt gp {43,79} 1 4 5 txt gp {47,79} 2 1 3 txt gp {53,79} 1 1 2 txt gp {59,79} 2 1 3 txt gp {61,79} 1 4 5 txt gp {67,79} 1 4 5 txt gp {71,79} 2 1 3 txt gp {73,79} 3 4 7 txt gp {2,83} 2 2 txt gp {3,83} 6 1 7 txt gp {5,83} 4 4 txt gp {7,83} 2 1 3 txt gp {11,83} 2 2 txt gp {13,83} 1 1 2 txt gp {17,83} 1 1 txt gp {19,83} 1 1 2 txt gp {23,83} 5 5 txt gp {29,83} 1 1 txt gp {31,83} 2 1 3 txt gp {37,83} 1 1 2 txt gp {41,83} 1 1 txt gp {43,83} 2 1 3 txt gp {47,83} 1 1 txt gp {53,83} 2 2 txt gp {59,83} 2 2 txt gp {61,83} 5 1 6 txt gp {67,83} 1 1 2 txt gp {71,83} 1 1 txt gp {73,83} 1 1 2 txt gp {79,83} 2 1 3 txt gp {2,89} 1 1 txt gp {3,89} 5 1 6 txt gp {5,89} 0 {7,89} 1 1 2 txt gp {11,89} 0 {13,89} 1 1 txt gp {17,89} 0 {19,89} 2 1 3 txt gp {23,89} 2 2 txt gp {29,89} 1 1 txt gp {31,89} 2 1 3 txt gp {37,89} 1 1 2 txt gp {41,89} 0 {43,89} 1 1 2 txt gp {47,89} 0 {53,89} 0 {59,89} 1 1 txt gp {61,89} 1 1 2 txt gp {67,89} 1 1 2 txt gp {71,89} 0 {73,89} 1 1 txt gp {79,89} 1 1 2 txt gp {83,89} 5 5 txt gp {2,97} 2 1 3 txt gp {3,97} 8 4 12 txt gp {5,97} 1 1 txt gp {7,97} 1 4 5 txt gp {11,97} 2 1 3 txt gp {13,97} 4 4 txt gp {17,97} 1 1 txt gp {19,97} 1 4 5 txt gp {23,97} 2 1 3 txt gp {29,97} 1 1 2 txt gp {31,97} 5 4 9 txt gp {37,97} 4 4 txt gp {41,97} 1 1 txt gp {43,97} 1 4 5 txt gp {47,97} 2 1 3 txt gp {53,97} 1 1 txt gp {59,97} 2 1 3 txt gp {61,97} 4 4 txt gp {67,97} 4 4 txt gp {71,97} 1 1 2 txt gp {73,97} 4 4 txt gp {79,97} 1 4 5 txt gp {83,97} 1 1 2 txt gp {89,97} 1 1 txt gp {2,101} 3 3 txt gp {3,101} 5 1 6 txt gp {5,101} 0 {7,101} 2 1 3 txt gp {11,101} 1 1 txt gp {13,101} 1 1 txt gp {17,101} 0 {19,101} 1 1 txt gp {23,101} 1 1 txt gp {29,101} 0 {31,101} 1 1 2 txt gp {37,101} 1 1 txt gp {41,101} 0 {43,101} 1 1 2 txt gp {47,101} 0 {53,101} 1 1 txt gp {59,101} 2 2 txt gp {61,101} 1 1 2 txt gp {67,101} 1 1 2 txt gp {71,101} 0 {73,101} 1 1 2 txt gp {79,101} 1 1 txt gp {83,101} 1 1 txt gp {89,101} 1 1 txt gp {97,101} 1 1 2 txt gp {2,103} 1 1 2 txt gp {3,103} 5 4 9 txt gp {5,103} 2 1 3 txt gp {7,103} 1 4 5 txt gp {11,103} 2 1 3 txt gp {13,103} 1 4 5 txt gp {17,103} 1 1 2 txt gp {19,103} 2 4 6 txt gp {23,103} 1 1 2 txt gp {29,103} 1 1 2 txt gp {31,103} 1 4 5 txt gp {37,103} 4 4 txt gp {41,103} 1 1 txt gp {43,103} 1 4 5 txt gp {47,103} 3 1 4 txt gp {53,103} 1 1 2 txt gp {59,103} 1 1 2 txt gp {61,103} 2 4 6 txt gp {67,103} 2 4 6 txt gp {71,103} 2 1 3 txt gp {73,103} 4 4 txt gp {79,103} 1 4 5 txt gp {83,103} 1 1 2 txt gp {89,103} 2 1 3 txt gp {97,103} 1 4 5 txt gp {101,103} 2 1 3 txt gp {2,107} 3 3 txt gp {3,107} 9 1 10 txt gp {5,107} 2 2 txt gp {7,107} 1 1 2 txt gp {11,107} 2 2 txt gp {13,107} 1 1 2 txt gp {17,107} 1 1 txt gp {19,107} 2 1 3 txt gp {23,107} 2 2 txt gp {29,107} 1 1 txt gp {31,107} 2 1 3 txt gp {37,107} 1 1 2 txt gp {41,107} 1 1 txt gp {43,107} 1 1 2 txt gp {47,107} 2 2 txt gp {53,107} 1 1 txt gp {59,107} 5 5 txt gp {61,107} 1 1 2 txt gp {67,107} 1 1 2 txt gp {71,107} 1 1 txt gp {73,107} 3 1 4 txt gp {79,107} 5 1 6 txt gp {83,107} 2 2 txt gp {89,107} 2 2 txt gp {97,107} 2 1 3 txt gp {101,107} 2 2 txt gp {103,107} 1 1 2 txt gp {2,109} 2 1 3 txt gp {3,109} 9 4 13 txt gp {5,109} 1 1 txt gp {7,109} 1 4 5 txt gp {11,109} 1 1 2 txt gp {13,109} 4 4 txt gp {17,109} 1 1 txt gp {19,109} 1 4 5 txt gp {23,109} 1 1 2 txt gp {29,109} 1 1 txt gp {31,109} 1 4 5 txt gp {37,109} 4 4 txt gp {41,109} 1 1 txt gp {43,109} 1 4 5 txt gp {47,109} 1 1 txt gp {53,109} 1 1 2 txt gp {59,109} 2 1 3 txt gp {61,109} 4 4 txt gp {67,109} 1 4 5 txt gp {71,109} 1 1 2 txt gp {73,109} 4 4 txt gp {79,109} 4 4 txt gp {83,109} 1 1 2 txt gp {89,109} 1 1 txt gp {97,109} 4 4 txt gp {101,109} 1 1 2 txt gp {103,109} 4 4 txt gp {107,109} 1 1 2 txt gp {2,113} 0 {3,113} 6 1 7 txt gp {5,113} 1 1 txt gp {7,113} 1 1 txt gp {11,113} 0 {13,113} 1 1 txt gp {17,113} 1 1 txt gp {19,113} 1 1 2 txt gp {23,113} 5 5 txt gp {29,113} 1 1 txt gp {31,113} 1 1 2 txt gp {37,113} 1 1 txt gp {41,113} 0 {43,113} 2 1 3 txt gp {47,113} 2 2 txt gp {53,113} 0 {59,113} 1 1 txt gp {61,113} 1 1 txt gp {67,113} 2 1 3 txt gp {71,113} 1 1 txt gp {73,113} 1 1 2 txt gp {79,113} 1 1 2 txt gp {83,113} 2 2 txt gp {89,113} 1 1 txt gp {97,113} 1 1 2 txt gp {101,113} 0 {103,113} 1 1 2 txt gp {107,113} 1 1 txt gp {109,113} 1 1 2 txt gp {2,127} 1 1 2 txt gp {3,127} 5 4 9 txt gp {5,127} 1 1 2 txt gp {7,127} 1 4 5 txt gp {11,127} 1 1 txt gp {13,127} 1 4 5 txt gp {17,127} 2 1 3 txt gp {19,127} 1 4 5 txt gp {23,127} 2 1 3 txt gp {29,127} 1 1 2 txt gp {31,127} 2 4 6 txt gp {37,127} 2 4 6 txt gp {41,127} 1 1 txt gp {43,127} 1 4 5 txt gp {47,127} 1 1 txt gp {53,127} 1 1 2 txt gp {59,127} 2 1 3 txt gp {61,127} 2 4 6 txt gp {67,127} 1 4 5 txt gp {71,127} 1 1 txt gp {73,127} 2 4 6 txt gp {79,127} 1 4 5 txt gp {83,127} 2 1 3 txt gp {89,127} 1 1 2 txt gp {97,127} 1 4 5 txt gp {101,127} 2 1 3 txt gp {103,127} 1 4 5 txt gp {107,127} 2 1 3 txt gp {109,127} 4 4 txt gp {113,127} 2 1 3 txt gp {2,131} 3 3 txt gp {3,131} 6 1 7 txt gp {5,131} 1 1 txt gp {7,131} 2 1 3 txt gp {11,131} 1 1 txt gp {13,131} 1 1 2 txt gp {17,131} 2 2 txt gp {19,131} 1 1 txt gp {23,131} 2 2 txt gp {29,131} 1 1 txt gp {31,131} 1 1 2 txt gp {37,131} 1 1 2 txt gp {41,131} 1 1 txt gp {43,131} 2 1 3 txt gp {47,131} 1 1 txt gp {53,131} 1 1 txt gp {59,131} 4 4 txt gp {61,131} 1 1 2 txt gp {67,131} 1 1 txt gp {71,131} 2 2 txt gp {73,131} 1 1 2 txt gp {79,131} 1 1 txt gp {83,131} 2 2 txt gp {89,131} 0 {97,131} 1 1 txt gp {101,131} 1 1 txt gp {103,131} 1 1 txt gp {107,131} 1 1 txt gp {109,131} 2 1 3 txt gp {113,131} 0 {127,131} 1 1 txt gp {2,137} 1 1 txt gp {3,137} 6 1 7 txt gp {5,137} 0 {7,137} 1 1 2 txt gp {11,137} 0 {13,137} 1 1 2 txt gp {17,137} 0 {19,137} 1 1 txt gp {23,137} 4 4 txt gp {29,137} 2 2 txt gp {31,137} 4 1 5 txt gp {37,137} 1 1 txt gp {41,137} 1 1 txt gp {43,137} 1 1 2 txt gp {47,137} 1 1 txt gp {53,137} 1 1 txt gp {59,137} 1 1 txt gp {61,137} 1 1 txt gp {67,137} 1 1 2 txt gp {71,137} 2 2 txt gp {73,137} 1 1 txt gp {79,137} 1 1 2 txt gp {83,137} 2 2 txt gp {89,137} 0 {97,137} 1 1 txt gp {101,137} 0 {103,137} 1 1 2 txt gp {107,137} 1 1 txt gp {109,137} 1 1 2 txt gp {113,137} 0 {127,137} 5 1 6 txt gp {131,137} 1 1 txt gp {2,139} 2 1 3 txt gp {3,139} 6 4 10 txt gp {5,139} 3 1 4 txt gp {7,139} 1 4 5 txt gp {11,139} 1 1 2 txt gp {13,139} 2 4 6 txt gp {17,139} 1 1 2 txt gp {19,139} 2 4 6 txt gp {23,139} 5 1 6 txt gp {29,139} 2 1 3 txt gp {31,139} 5 4 9 txt gp {37,139} 5 4 9 txt gp {41,139} 2 1 3 txt gp {43,139} 2 4 6 txt gp {47,139} 1 1 2 txt gp {53,139} 1 1 2 txt gp {59,139} 2 1 3 txt gp {61,139} 1 4 5 txt gp {67,139} 1 4 5 txt gp {71,139} 2 1 3 txt gp {73,139} 1 4 5 txt gp {79,139} 4 4 8 txt gp {83,139} 2 1 3 txt gp {89,139} 1 1 2 txt gp {97,139} 1 4 5 txt gp {101,139} 5 1 6 txt gp {103,139} 2 4 6 txt gp {107,139} 2 1 3 txt gp {109,139} 1 4 5 txt gp {113,139} 1 1 2 txt gp {127,139} 1 4 5 txt gp {131,139} 1 1 2 txt gp {137,139} 2 1 3 txt gp {2,149} 2 2 txt gp {3,149} 5 1 6 txt gp {5,149} 0 {7,149} 1 1 txt gp {11,149} 1 1 txt gp {13,149} 1 1 2 txt gp {17,149} 0 {19,149} 1 1 2 txt gp {23,149} 5 5 txt gp {29,149} 0 {31,149} 2 1 3 txt gp {37,149} 1 1 txt gp {41,149} 1 1 txt gp {43,149} 1 1 2 txt gp {47,149} 0 {53,149} 0 {59,149} 5 5 txt gp {61,149} 1 1 2 txt gp {67,149} 1 1 2 txt gp {71,149} 1 1 txt gp {73,149} 1 1 2 txt gp {79,149} 2 1 3 txt gp {83,149} 2 2 txt gp {89,149} 0 {97,149} 1 1 txt gp {101,149} 1 1 txt gp {103,149} 1 1 txt gp {107,149} 2 2 txt gp {109,149} 1 1 txt gp {113,149} 0 {127,149} 1 1 2 txt gp {131,149} 2 2 txt gp {137,149} 2 2 txt gp {139,149} 2 1 3 txt gp {2,151} 1 1 2 txt gp {3,151} 5 4 9 txt gp {5,151} 2 1 3 txt gp {7,151} 1 4 5 txt gp {11,151} 1 1 txt gp {13,151} 1 4 5 txt gp {17,151} 1 1 txt gp {19,151} 1 4 5 txt gp {23,151} 5 1 6 txt gp {29,151} 1 1 2 txt gp {31,151} 2 4 6 txt gp {37,151} 1 4 5 txt gp {41,151} 1 1 2 txt gp {43,151} 1 4 5 txt gp {47,151} 1 1 txt gp {53,151} 1 1 2 txt gp {59,151} 2 1 3 txt gp {61,151} 1 4 5 txt gp {67,151} 1 4 5 txt gp {71,151} 3 1 4 txt gp {73,151} 1 4 5 txt gp {79,151} 1 4 5 txt gp {83,151} 2 1 3 txt gp {89,151} 2 1 3 txt gp {97,151} 1 4 5 txt gp {101,151} 1 1 2 txt gp {103,151} 1 4 5 txt gp {107,151} 2 1 3 txt gp {109,151} 4 4 txt gp {113,151} 1 1 2 txt gp {127,151} 1 4 5 txt gp {131,151} 2 1 3 txt gp {137,151} 1 1 txt gp {139,151} 2 4 6 txt gp {149,151} 2 1 3 txt gp

## Cases where S contains three primes

 S S3 C3 Total {2,3,5} 31 1 32 txt gp {2,3,7} 30 4 34 txt gp {2,5,7} 6 1 7 txt gp {3,5,7} 20 4 24 txt gp {2,3,11} 35 1 36 txt gp {2,5,11} 7 7 txt gp {3,5,11} 23 1 24 txt gp {2,7,11} 5 1 6 txt gp {3,7,11} 19 4 23 txt gp {5,7,11} 2 1 3 txt gp {2,3,13} 30 4 34 txt gp {2,5,13} 6 1 7 txt gp {3,5,13} 20 4 24 txt gp {2,7,13} 6 4 10 txt gp {3,7,13} 19 13 32 txt gp {5,7,13} 2 4 6 txt gp {2,11,13} 9 1 10 txt gp {3,11,13} 22 4 26 txt gp {5,11,13} 3 1 4 txt gp {7,11,13} 3 4 7 txt gp {2,3,17} 35 1 36 txt gp {2,5,17} 6 6 txt gp {3,5,17} 22 1 23 txt gp {2,7,17} 5 1 6 txt gp {3,7,17} 20 4 24 txt gp {5,7,17} 4 1 5 txt gp {2,11,17} 9 9 txt gp {3,11,17} 21 1 22 txt gp {5,11,17} 3 3 txt gp {7,11,17} 5 1 6 txt gp {2,13,17} 3 1 4 txt gp {3,13,17} 32 4 36 txt gp {5,13,17} 1 1 2 txt gp {7,13,17} 3 4 7 txt gp {11,13,17} 4 1 5 txt gp {2,3,19} 34 4 38 txt gp {2,5,19} 8 1 9 txt gp {3,5,19} 22 4 26 txt gp {2,7,19} 7 4 11 txt gp {3,7,19} 23 13 36 txt gp {5,7,19} 3 4 7 txt gp {2,11,19} 10 1 11 txt gp {3,11,19} 18 4 22 txt gp {5,11,19} 1 1 txt gp {7,11,19} 1 4 5 txt gp {2,13,19} 7 4 11 txt gp {3,13,19} 20 13 33 txt gp {5,13,19} 3 4 7 txt gp {7,13,19} 3 13 16 txt gp {11,13,19} 3 4 7 txt gp {2,17,19} 5 1 6 txt gp {3,17,19} 22 4 26 txt gp {5,17,19} 5 1 6 txt gp {7,17,19} 2 4 6 txt gp {11,17,19} 3 1 4 txt gp {13,17,19} 2 4 6 txt gp {2,3,23} 37 1 38 txt gp {2,5,23} 9 9 txt gp {3,5,23} 21 1 22 txt gp {2,7,23} 3 1 4 txt gp {3,7,23} 18 4 22 txt gp {5,7,23} 4 1 5 txt gp {2,11,23} 8 8 txt gp {3,11,23} 28 1 29 txt gp {5,11,23} 6 6 txt gp {7,11,23} 1 1 2 txt gp {2,13,23} 9 1 10 txt gp {3,13,23} 36 4 40 txt gp {5,13,23} 5 1 6 txt gp {7,13,23} 2 4 6 txt gp {11,13,23} 5 1 6 txt gp {2,17,23} 6 6 txt gp {3,17,23} 21 1 22 txt gp {5,17,23} 7 7 txt gp {7,17,23} 4 1 5 txt gp {11,17,23} 7 7 txt gp {13,17,23} 7 1 8 txt gp {2,19,23} 12 1 13 txt gp {3,19,23} 18 4 22 txt gp {5,19,23} 3 1 4 txt gp {7,19,23} 3 4 7 txt gp {11,19,23} 2 1 3 txt gp {13,19,23} 3 4 7 txt gp {17,19,23} 3 1 4 txt gp {2,3,29} 32 1 33 txt gp {2,5,29} 8 8 txt gp {3,5,29} 26 1 27 txt gp {2,7,29} 6 1 7 txt gp {3,7,29} 22 4 26 txt gp {5,7,29} 2 1 3 txt gp {2,11,29} 10 10 txt gp {3,11,29} 21 1 22 txt gp {5,11,29} 2 2 txt gp {7,11,29} 4 1 5 txt gp {2,13,29} 6 1 7 txt gp {3,13,29} 32 4 36 txt gp {5,13,29} 1 1 txt gp {7,13,29} 1 4 5 txt gp {11,13,29} 5 1 6 txt gp {2,17,29} 7 7 txt gp {3,17,29} 21 1 22 txt gp {5,17,29} 2 2 txt gp {7,17,29} 4 1 5 txt gp {11,17,29} 6 6 txt gp {13,17,29} 2 1 3 txt gp {2,19,29} 11 1 12 txt gp {3,19,29} 21 4 25 txt gp {5,19,29} 2 1 3 txt gp {7,19,29} 6 4 10 txt gp {11,19,29} 4 1 5 txt gp {13,19,29} 2 4 6 txt gp {17,19,29} 3 1 4 txt gp {2,23,29} 11 11 txt gp {3,23,29} 24 1 25 txt gp {5,23,29} 2 2 txt gp {7,23,29} 1 1 2 txt gp {11,23,29} 3 3 txt gp {13,23,29} 2 1 3 txt gp {17,23,29} 4 4 txt gp {19,23,29} 3 1 4 txt gp {2,3,31} 31 4 35 txt gp {2,5,31} 6 1 7 txt gp {3,5,31} 22 4 26 txt gp {2,7,31} 4 4 8 txt gp {3,7,31} 23 13 36 txt gp {5,7,31} 2 4 6 txt gp {2,11,31} 9 1 10 txt gp {3,11,31} 27 4 31 txt gp {5,11,31} 4 1 5 txt gp {7,11,31} 6 4 10 txt gp {2,13,31} 6 4 10 txt gp {3,13,31} 20 13 33 txt gp {5,13,31} 3 4 7 txt gp {7,13,31} 2 13 15 txt gp {11,13,31} 3 4 7 txt gp {2,17,31} 5 1 6 txt gp {3,17,31} 21 4 25 txt gp {5,17,31} 4 1 5 txt gp {7,17,31} 7 4 11 txt gp {11,17,31} 10 1 11 txt gp {13,17,31} 4 4 8 txt gp {2,19,31} 5 4 9 txt gp {3,19,31} 23 13 36 txt gp {5,19,31} 3 4 7 txt gp {7,19,31} 6 13 19 txt gp {11,19,31} 7 4 11 txt gp {13,19,31} 5 13 18 txt gp {17,19,31} 7 4 11 txt gp {2,23,31} 7 1 8 txt gp {3,23,31} 27 4 31 txt gp {5,23,31} 7 1 8 txt gp {7,23,31} 5 4 9 txt gp {11,23,31} 9 1 10 txt gp {13,23,31} 6 4 10 txt gp {17,23,31} 9 1 10 txt gp {19,23,31} 6 4 10 txt gp {2,29,31} 8 1 9 txt gp {3,29,31} 22 4 26 txt gp {5,29,31} 2 1 3 txt gp {7,29,31} 7 4 11 txt gp {11,29,31} 8 1 9 txt gp {13,29,31} 2 4 6 txt gp {17,29,31} 6 1 7 txt gp {19,29,31} 7 4 11 txt gp {23,29,31} 6 1 7 txt gp {2,3,37} 31 4 35 txt gp {2,5,37} 7 1 8 txt gp {3,5,37} 20 4 24 txt gp {2,7,37} 4 4 8 txt gp {3,7,37} 33 13 46 txt gp {5,7,37} 6 4 10 txt gp {2,11,37} 11 1 12 txt gp {3,11,37} 36 4 40 txt gp {5,11,37} 2 1 3 txt gp {7,11,37} 2 4 6 txt gp {2,13,37} 7 4 11 txt gp {3,13,37} 25 13 38 txt gp {5,13,37} 1 4 5 txt gp {7,13,37} 2 13 15 txt gp {11,13,37} 4 4 8 txt gp {2,17,37} 7 1 8 txt gp {3,17,37} 20 4 24 txt gp {5,17,37} 1 1 2 txt gp {7,17,37} 5 4 9 txt gp {11,17,37} 6 1 7 txt gp {13,17,37} 2 4 6 txt gp {2,19,37} 8 4 12 txt gp {3,19,37} 19 13 32 txt gp {5,19,37} 2 4 6 txt gp {7,19,37} 4 13 17 txt gp {11,19,37} 2 4 6 txt gp {13,19,37} 3 13 16 txt gp {17,19,37} 2 4 6 txt gp {2,23,37} 10 1 11 txt gp {3,23,37} 22 4 26 txt gp {5,23,37} 4 1 5 txt gp {7,23,37} 4 4 8 txt gp {11,23,37} 4 1 5 txt gp {13,23,37} 3 4 7 txt gp {17,23,37} 3 1 4 txt gp {19,23,37} 3 4 7 txt gp {2,29,37} 8 1 9 txt gp {3,29,37} 21 4 25 txt gp {5,29,37} 2 1 3 txt gp {7,29,37} 4 4 8 txt gp {11,29,37} 6 1 7 txt gp {13,29,37} 1 4 5 txt gp {17,29,37} 2 1 3 txt gp {19,29,37} 2 4 6 txt gp {23,29,37} 4 1 5 txt gp {2,31,37} 8 4 12 txt gp {3,31,37} 21 13 34 txt gp {5,31,37} 6 4 10 txt gp {7,31,37} 7 13 20 txt gp {11,31,37} 6 4 10 txt gp {13,31,37} 4 13 17 txt gp {17,31,37} 6 4 10 txt gp {19,31,37} 4 13 17 txt gp {23,31,37} 3 4 7 txt gp {29,31,37} 3 4 7 txt gp {2,3,41} 36 1 37 txt gp {2,5,41} 2 2 txt gp {3,5,41} 25 1 26 txt gp {2,7,41} 6 1 7 txt gp {3,7,41} 20 4 24 txt gp {5,7,41} 6 1 7 txt gp {2,11,41} 8 8 txt gp {3,11,41} 22 1 23 txt gp {5,11,41} 3 3 txt gp {7,11,41} 7 1 8 txt gp {2,13,41} 9 1 10 txt gp {3,13,41} 21 4 25 txt gp {5,13,41} 1 1 2 txt gp {7,13,41} 3 4 7 txt gp {11,13,41} 6 1 7 txt gp {2,17,41} 7 7 txt gp {3,17,41} 22 1 23 txt gp {5,17,41} 3 3 txt gp {7,17,41} 6 1 7 txt gp {11,17,41} 8 8 txt gp {13,17,41} 4 1 5 txt gp {2,19,41} 9 1 10 txt gp {3,19,41} 20 4 24 txt gp {5,19,41} 2 1 3 txt gp {7,19,41} 6 4 10 txt gp {11,19,41} 7 1 8 txt gp {13,19,41} 6 4 10 txt gp {17,19,41} 5 1 6 txt gp {2,23,41} 5 5 txt gp {3,23,41} 23 1 24 txt gp {5,23,41} 3 3 txt gp {7,23,41} 4 1 5 txt gp {11,23,41} 3 3 txt gp {13,23,41} 3 1 4 txt gp {17,23,41} 5 5 txt gp {19,23,41} 3 1 4 txt gp {2,29,41} 7 7 txt gp {3,29,41} 24 1 25 txt gp {5,29,41} 2 2 txt gp {7,29,41} 4 1 5 txt gp {11,29,41} 8 8 txt gp {13,29,41} 2 1 3 txt gp {17,29,41} 4 4 txt gp {19,29,41} 6 1 7 txt gp {23,29,41} 4 4 txt gp {2,31,41} 1 1 2 txt gp {3,31,41} 22 4 26 txt gp {5,31,41} 2 1 3 txt gp {7,31,41} 3 4 7 txt gp {11,31,41} 7 1 8 txt gp {13,31,41} 4 4 8 txt gp {17,31,41} 4 1 5 txt gp {19,31,41} 4 4 8 txt gp {23,31,41} 4 1 5 txt gp {29,31,41} 5 1 6 txt gp {2,37,41} 4 1 5 txt gp {3,37,41} 32 4 36 txt gp {5,37,41} 1 1 txt gp {7,37,41} 6 4 10 txt gp {11,37,41} 7 1 8 txt gp {13,37,41} 2 4 6 txt gp {17,37,41} 2 1 3 txt gp {19,37,41} 3 4 7 txt gp {23,37,41} 2 1 3 txt gp {29,37,41} 3 1 4 txt gp {31,37,41} 4 4 8 txt gp

## Cases where S contains four primes

 S S3 C3 Total {2,3,5,7} 104 4 108 txt gp {2,3,5,11} 105 1 106 txt gp {2,3,7,11} 110 4 114 txt gp {2,5,7,11} 23 1 24 txt gp {3,5,7,11} 70 4 74 txt gp {2,3,5,13} 110 4 114 txt gp {2,3,7,13} 102 13 115 txt gp {2,5,7,13} 22 4 26 txt gp {3,5,7,13} 67 13 80 txt gp {2,3,11,13} 117 4 121 txt gp {2,5,11,13} 27 1 28 txt gp {3,5,11,13} 70 4 74 txt gp {2,7,11,13} 27 4 31 txt gp {3,7,11,13} 67 13 80 txt gp {5,7,11,13} 15 4 19 txt gp {2,3,5,17} 111 1 112 txt gp {2,3,7,17} 111 4 115 txt gp {2,5,7,17} 27 1 28 txt gp {3,5,7,17} 82 4 86 txt gp {2,3,11,17} 127 1 128 txt gp {2,5,11,17} 29 29 txt gp {3,5,11,17} 71 1 72 txt gp {2,7,11,17} 28 1 29 txt gp {3,7,11,17} 71 4 75 txt gp {5,7,11,17} 14 1 15 txt gp {2,3,13,17} 118 4 122 txt gp {2,5,13,17} 22 1 23 txt gp {3,5,13,17} 79 4 83 txt gp {2,7,13,17} 25 4 29 txt gp {3,7,13,17} 78 13 91 txt gp {5,7,13,17} 11 4 15 txt gp {2,11,13,17} 23 1 24 txt gp {3,11,13,17} 78 4 82 txt gp {5,11,13,17} 15 1 16 txt gp {7,11,13,17} 16 4 20 txt gp