Since you are new to JMP, I am reluctant to show you this option that might work for you.
JMP data table columns have multiple properties that can be set. Value Ordering that allows you to set the order of nominal axes instead of the default alphabetical order is probably the most used ( ex. Never, Seldom, Sometimes, Frequent, Always).
Another popular column property is Value Labels. This property can be set with a JMP script (JSL) or interactively.
Attached is a table with 2 columns x and y; and and an attached script called y vs. x. Use the inverted red triangle menu and select Run Script. It will create a GraphBuilder plot with only 1,2,3,6,9,12,18,24 labeled. But you will notice that the data table x values look strange.
You can select Column Info for x and uncheck use value labels. The graph will continue to have the limited labeling unless it is redrawn.
This is a method to create a custom graph axis that is good for generating the graph. I wouldn't use it for an interactive graph. This is the JSL syntax for the Value Labels. I set the X axis scale to be 0.5 to 24.5 with an increment of 1. Note the unwanted laebls are set to empty strings, and hence will not appear. You did not mention if you wanted these values to be equidistant, or linear spacing with limited labeling.
If your data only has your specified values (ex. a lifetime test, 1day 2, days, 3 days, etc.) another platform graph or a variability chart might be more useful. Interesting question.
:x << Value Labels(
{1 = "1", 2 = "2", 3 = "3", 4 = "", 5 = "", 6 = "6", 7 = "", 8 = "", 9
= "9", 10 = "", 11 = "", 12 = "12", 13 = "", 14 = "", 15 = "", 16 = "",
17 = "", 18 = "18", 19 = "", 20 = "", 21 = "", 22 = "", 23 = "", 24 =
"24"}
) << Use Value Labels( 1 );