>Every column that c appears in has what in common?
The first valid n (above 1) in said columns is always prime when c is coprime
c3637 (2, 3, 5 and 7 filtered)(7258,19)(7078,3539)(7018,11)(6598,3299)(5158,2579)(4358,2179)(4138,2069)(3674,11)(2918,1459)(1798,29)(874,19)(218,109)c6107 (n = 2, 3 and 5 filtered)(12214,31)(12178,6089)(11638,11)(11314,5657)(9298,4649)(8614,59)(7858,3929)(5158,2579)(4114,11)(2998,1499)...
When c has three factors, the first valid n in the e=c*2 column is always one of the factors.
c135336263417 (392956576089)(270672526834,1)(270672526834,3929)c447791149 (1356576089)(895582298,1)(895582298,13)c6380123599 (56930833637)(12760247198,1)(12760247198,569)c240520532961377359853213671 (1233232127918610991654346153)(481041065922754719706427342,1)...gap...(481041065922754719706427342,123323)
Not a direct calculation but haven't found any values where the above isn't true yet.