A list of all primitive quads like this is hard to find on the web.

Primitive quads starting with the smallest side of (1) up too (88)
(*) = primitive
(1,2,2,3)*
(1,4,8,9)*
(1,6,18,19)*
(1,8,32,33)*
(1,10,50,51)*
(1,12,12,17)*
(1,12,72,73)*
(1,14,98,99)*
(1,18,30,35)*
(1,22,46,51)*
(1,28,76,81)*
(1,32,100,105)*
(1,34,38,51)*
(1,44,68,81)*
(1,68,80,105)*
(1,70,70,99)*
(2,3,6,7)*
(2,5,14,15)*
(2,6,9,11)*
(2,7,26,27)*
(2,9,42,43)*
(2,10,11,15)*
(2,10,25,27)*
(2,11,62,63)*
(2,13,86,87)*
(2,14,23,27)*
(2,14,49,51)*
(2,18,39,43)*
(2,18,81,83)*
(2,19,34,39)*
(2,21,42,47)*
(2,22,59,63)*
(2,26,29,39)*
(2,26,83,87)*
(2,29,82,87)*
(2,31,94,99)*
(2,34,53,63)*
(2,43,46,63)*
(2,44,92,102)
(2,49,86,99)*
(2,54,63,83)*
(2,59,94,111)*
(2,61,62,87)*
(2,66,99,119)*
(3,4,12,13)*
(3,6,22,23)*
(3,8,36,37)*
(3,10,54,55)*
(3,12,76,77)*
(3,14,18,23)*
(3,16,24,29)*
(3,24,28,37)*
(3,24,56,61)*
(3,26,66,71)*
(3,30,46,55)*
(3,36,68,77)*
(3,42,94,103)*
(3,46,54,71)*
(3,50,90,103)*
(3,56,84,101)*
(3,80,96,125)*
(3,92,96,133)*
(4,4,7,9)*
(4,5,20,21)*
(4,7,32,33)*
(4,8,19,21)*
(4,9,48,49)*
(4,11,68,69)*
(4,12,39,41)*
(4,13,16,21)*
(4,13,92,93)*
(4,16,67,69)*
(4,17,28,33)*
(4,23,52,57)*
(4,24,33,41)*
(4,27,72,77)*
(4,28,35,45)*
(4,32,47,57)*
(4,32,61,69)*
(4,33,36,49)*
(4,40,97,105)*
(4,44,53,69)*
(4,45,72,85)*
(4,52,77,93)*
(4,72,87,113)*
(4,77,88,117)*
(4,84,87,121)*
(5,6,30,31)*
(5,8,44,45)*
(5,10,62,63)*
(5,12,84,85)*
(5,38,50,63)*
(5,40,56,69)*
(5,48,60,77)*
(5,54,78,95)*
(5,70,86,111)*
(6,6,7,11)*
(6,6,17,19)*
(6,7,42,43)*
(6,9,18,21)*
(6,9,58,59)*
(6,10,15,19)*
(6,10,33,35)*
(6,11,78,79)*
(6,13,18,23)*
(6,14,27,31)*
(6,14,57,59)*
(6,15,42,45)*
(6,17,30,35)*
(6,18,27,33)*
(6,18,43,47)*
(6,18,89,91)*
(6,21,22,31)*
(6,21,78,81)*
(6,22,63,67)*
(6,23,54,59)*
(6,26,87,91)*
(6,27,38,47)*
(6,27,74,79)*
(6,33,58,67)*
(6,35,42,55)*
(6,38,69,79)*
(6,39,82,91)*
(6,41,42,59)*
(6,42,85,95)*
(6,43,66,79)*
(6,54,73,91)*
(6,58,75,95)*
(6,62,87,107)*
(6,67,78,103)*
(6,73,78,107)*
(6,74,93,119)*
(6,90,95,131)*
(7,8,56,57)*
(7,10,74,75)*
(7,12,96,97)*
(7,14,22,27)*
(7,16,28,33)*
(7,24,60,65)*
(7,26,70,75)*
(7,30,30,43)*
(7,40,40,57)*
(7,48,84,97)*
(7,74,98,123)*
(8,8,31,33)*
(8,9,12,17)*
(8,9,72,73)*
(8,11,16,21)*
(8,11,92,93)*
(8,12,51,53)*
(8,16,79,81)*
(8,21,48,53)*
(8,24,27,37)*
(8,28,49,57)*
(8,29,88,93)*
(8,31,100,105)*
(8,36,63,73)*
(8,36,81,89)*
(8,44,95,105)*
(8,49,64,81)*
(8,51,96,109)*
(8,53,76,93)*
(8,64,67,93)*
(8,69,84,109)*
(8,80,85,117)*
(9,10,90,91)*
(9,12,20,25)*
(9,18,38,43)*
(9,22,54,59)*
(9,24,32,41)*
(9,28,84,89)*
(9,30,50,59)*
(9,32,36,49)*
(9,42,98,107)*
(9,46,78,91)*
(9,62,66,91)*
(10,10,23,27)*
(10,10,49,51)*
(10,14,35,39)*
(10,14,73,75)*
(10,18,51,55)*
(10,22,71,75)*
(10,26,95,99)*
(10,37,50,63)*
(10,41,62,75)*
(10,45,54,71)*
(10,57,90,107)*
(10,65,74,99)*
(11,12,24,29)*
(11,18,42,47)*
(11,22,22,33)*
(11,22,58,63)*
(11,28,88,93)*
(11,36,48,61)*
(11,42,66,79)*
(11,44,52,69)*
(11,58,94,111)*
(11,74,82,111)*
(12,12,71,73)*
(12,14,84,86)*
(12,15,16,25)*
(12,16,21,29)*
(12,16,99,101)*
(12,19,48,53)*
(12,21,28,37)*
(12,21,56,61)*
(12,24,31,41)*
(12,24,41,49)*
(12,27,44,53)*
(12,29,96,101)*
(12,31,36,49)*
(12,32,69,77)*
(12,33,64,73)*
(12,36,37,53)*
(12,36,67,77)*
(12,39,88,97)*
(12,44,57,73)*
(12,44,99,109)*
(12,47,84,97)*
(12,48,59,77)*
(12,52,81,97)*
(12,59,60,85)*
(12,60,95,113)*
(12,88,99,133)*
(12,96,97,137)*
(13,14,34,39)*
(13,16,40,45)*
(13,24,72,77)*
(13,26,82,87)*
(13,50,70,87)*
(13,52,76,93)*
(13,66,78,103)*
(13,76,88,117)*
(14,14,47,51)*
(14,14,97,99)*
(14,17,46,51)*
(14,18,21,31)*
(14,18,63,67)*
(14,22,29,39)*
(14,22,83,87)*
(14,23,70,75)*
(14,27,90,95)*
(14,31,38,51)*
(14,35,98,105)*
(14,38,77,87)*
(14,39,42,59)*
(14,42,63,77)*
(14,42,93,103)*
(14,47,86,99)*
(14,58,79,99)*
(14,62,91,111)*
(14,70,85,111)*
(14,73,98,123)*
(15,18,26,35)*
(15,24,40,49)*
(15,30,58,67)*
(15,36,52,65)*
(15,36,80,89)*
(15,42,50,67)*
(15,42,70,83)*
(15,60,64,89)*
(15,90,94,131)*
(16,17,52,57)*
(16,20,37,45)*
(16,23,76,81)*
(16,27,96,101)*
(16,28,47,57)*
(16,28,61,69)*
(16,32,59,69)*
(16,36,93,101)*
(16,37,56,69)*
(16,41,68,81)*
(16,47,64,81)*
(16,55,88,105)*
(16,63,72,97)*
(16,69,72,101)*
(16,89,92,129)*
(17,20,20,33)*
(17,24,84,89)*
(17,26,94,99)*
(17,32,44,57)*
(17,46,86,99)*
(17,56,56,81)*
(18,18,79,83)*
(18,19,66,71)*
(18,21,38,47)*
(18,21,74,79)*
(18,22,99,103)*
(18,25,30,43)*
(18,26,45,55)*
(18,27,34,47)*
(18,33,74,83)*
(18,34,69,79)*
(18,39,98,107)*
(18,42,49,67)*
(18,46,51,71)*
(18,47,66,83)*
(18,51,90,105)
(18,54,71,91)*
(18,55,90,107)*
(18,66,77,103)*
(18,71,78,107)*
(19,22,26,39)*
(19,22,82,87)*
(19,30,42,55)*
(19,42,54,71)*
(19,48,96,109)*
(19,58,62,87)*
(20,24,57,65)*
(20,28,29,45)*
(20,32,85,93)*
(20,35,56,69)*
(20,36,45,61)*
(20,39,48,65)*
(20,43,80,93)*
(20,44,65,81)*
(20,52,89,105)*
(20,55,56,81)*
(20,79,100,129)*
(20,80,83,117)*
(21,22,90,95)*
(21,24,52,61)*
(21,28,84,91)*
(21,30,70,79)*
(21,36,92,101)*
(21,38,66,79)*
(21,40,72,85)*
(21,50,78,95)*
(21,52,84,101)*
(21,72,100,125)*
(21,78,98,127)*
(22,26,53,63)*
(22,31,34,51)*
(22,33,54,67)*
(22,34,77,87)*
(22,37,46,63)*
(22,45,90,103)*
(22,46,55,75)*
(22,54,75,95)*
(22,58,61,87)*
(22,71,98,123)*
(22,82,89,123)*
(23,24,24,41)*
(23,24,36,49)*
(23,28,44,57)*
(23,44,64,81)*
(23,64,80,105)*
(23,72,84,113)*
(23,84,84,121)*
(24,27,68,77)*
(24,28,63,73)*
(24,28,81,89)*
(24,29,48,61)*
(24,32,75,85)*
(24,33,88,97)*
(24,36,43,61)*
(24,45,68,85)*
(24,48,71,89)*
(24,57,64,89)*
(24,68,87,113)*
(24,80,93,125)*
(24,92,93,133)*
(25,32,40,57)*
(25,34,62,75)*
(25,36,48,65)*
(25,44,92,105)*
(25,60,72,97)*
(25,68,76,105)*
(25,70,98,123)*
(26,38,43,63)*
(26,39,78,91)*
(26,42,51,71)*
(26,49,82,99)*
(26,53,94,111)*
(26,57,66,91)*
(26,58,91,111)*
(26,65,70,99)*
(27,28,36,53)*
(27,30,86,95)*
(27,34,66,79)*
(27,40,60,77)*
(27,44,96,109)*
(27,64,84,109)*
(27,72,96,123)*
(27,88,96,133)*
(28,28,41,57)*
(28,36,57,73)*
(28,36,99,109)*
(28,41,64,81)*
(28,44,77,93)*
(28,68,91,117)*
(28,75,96,125)*
(29,48,84,101)*
(29,58,58,87)*
(30,30,41,59)*
(30,33,50,67)*
(30,33,70,83)*
(30,35,54,71)*
(30,42,65,83)*
(30,45,46,71)*
(30,54,97,115)*
(30,55,66,91)*
(30,58,69,95)*
(30,75,98,127)*
(30,78,79,115)*
(31,38,86,99)*
(31,40,92,105)*
(31,42,42,67)*
(31,46,82,99)*
(31,58,74,99)*
(31,90,90,131)*
(32,35,80,93)*
(32,43,76,93)*
(32,48,51,77)*
(32,49,56,81)*
(32,51,60,85)*
(32,56,67,93)*
(32,56,94,114)
(32,64,64,96)
(32,65,76,105)*
(32,72,81,113)*
(32,76,83,117)*
(32,80,100,132)
(32,81,84,121)*
(33,36,72,87)
(33,38,66,83)*
(33,44,48,73)*
(33,56,72,97)*
(33,66,66,99)
(33,68,84,113)*
(33,92,96,137)*
(34,37,38,63)*
(34,38,55,75)*
(34,40,40,66)
(34,42,63,83)*
(34,63,90,115)*
(34,64,88,114)
(34,66,93,119)*
(34,68,68,102)
(35,38,70,87)*
(35,40,44,69)*
(35,50,62,87)*
(35,60,84,109)*
(35,70,70,105)
(35,72,96,125)*
(35,86,98,135)*
(36,36,73,89)*
(36,37,96,109)*
(36,43,84,101)*
(36,44,93,109)*
(36,48,91,109)*
(36,55,60,89)*
(36,61,72,101)*
(36,76,87,121)*
(36,88,93,133)*
(37,46,94,111)*
(37,74,74,111)*
(38,41,50,75)*
(38,46,79,99)*
(38,54,99,119)*
(38,59,86,111)*
(39,48,64,89)*
(39,52,72,97)*
(39,54,62,91)*
(39,62,78,107)*
(40,41,88,105)*
(40,44,55,81)*
(40,45,48,77)*
(40,60,87,113)*
(40,64,73,105)*
(40,71,100,129)*
(40,91,100,141)*
(41,62,98,123)*
(42,42,89,107)*
(42,46,87,107)*
(42,47,54,83)*
(42,50,69,95)*
(42,54,77,103)*
(42,66,67,103)*
(42,66,73,107)*
(42,69,98,127)*
(42,70,81,115)*
(42,78,91,127)*
(42,81,94,131)*
(43,52,64,93)*
(43,64,88,117)*
(44,69,72,109)*
(44,79,92,129)*
(45,50,78,103)*
(46,47,74,99)*
(46,53,86,111)*
(46,54,57,91)*
(46,57,78,107)*
(46,59,82,111)*
(47,54,90,115)*
(47,60,60,97)*
(48,56,63,97)*
(48,56,69,101)*
(48,76,81,121)*
(48,84,97,137)*
(49,50,70,99)*
(49,72,72,113)*
(49,72,84,121)*
(49,76,92,129)*
(50,55,98,123)*
(50,81,90,131)*
(50,83,94,135)*
(51,64,72,109)*
(51,74,78,119)*
(52,53,56,93)*
(52,64,83,117)*
(52,72,99,133)*
(53,56,88,117)*
(53,60,96,125)*
(54,65,78,115)*
(54,66,83,119)*
(54,75,90,129)*
(54,87,94,139)*
(56,63,84,119)*
(56,64,97,129)*
(56,68,77,117)*
(56,71,92,129)*
(56,91,92,141)*
(57,62,66,107)*
(57,84,92,137)*
(58,59,74,111)*
(58,62,89,123)*
(58,71,82,123)*
(58,94,97,147)*
(59,80,100,141)*
(60,75,92,133)*
(61,66,78,119)*
(61,70,98,135)*
(63,66,70,115)*
(63,66,94,131)*
(63,84,88,137)*
(63,84,100,145)*
(64,68,89,129)*
(66,86,87,139)*
(67,70,94,135)*
(68,76,79,129)*
(69,72,88,133)*
(69,78,98,143)*
(70,70,73,123)*
(70,77,86,135)*
(70,90,99,151)*
(74,82,97,147)*
(75,82,90,143)*
(77,84,96,149)*
(80,84,87,145)*
(86,91,98,159)*
(88,88,89,153)*

Any errors or omissions?
Dan