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