Hi @Atheena,
Welcome in the Community !
There are no specific constraints about the interval between each level of a discrete numeric factor.
When creating your design, the only constraint is to maintain the numerical values ordering "These values have an implied order." : Factors (jmp.com)
So your levels should be ordered like 1, 5, 8, 15, ...
By default, for k levels of your discrete numeric factor, the assumed model by JMP may contain polynomial terms up to k-1 order (like in the screenshot taken, I have 4 levels in my X4 discrete numeric factor, so JMP has added in the model tab the terms X4*X4 and X4*X4*X4).
Note however that if you have strong differences between the intervals of your discrete numeric factor, this may affect the identification of statistically significant polynomial terms and the selection of an appropriate model, as it will be more difficult to find and fit a polynomial model if points are not homogeneously distributed.
Example here with data only close to the edges of the factor range, making it difficult to know which polynomial model complexity to choose :
In case of doubt during the modeling, visualize the data, try the more simple models, and confirm the chosen model with domain expertise and validation points.
I hope this answer will help you,