u/ConcernOk6623

I'm not even sure how to describe it other than (x+n)/n=prime

x	(x+1)/1	(x+2)/2	(x+3)/3	(x+4)/4	(x+5)/5
1	2
4	5	3
12	13	7	5
12720	12721	6361	4241	3181
19440	19441	9721	6481	4861	3889

and technically 720 also works for 4, but negative: 719, 359, 239, 179

but I haven't found one for 6 or more, and I haven't found anything about these numbers, either, and these are just the first/smallest ones I found as well