Create a new assignment

[tait1k27]

How to create a new trial factor assignment with \(M_p\) in Prime95, where \(M_p\) is a composite number

[kriesel]

Originally Posted by tait1k27

How to create a new trial factor assignment with \(M_p\) in Prime95, where \(M_p\) is a composite number

Well, for GIMPS prime finding purposes, or efficiency, don't.
If you already know M(p)=2^p-1 is composite, it's already ruled out as the next Mp discovery.
If it's the exponent that's composite, there are easily found algebraic factors for the corresponding Mn.
TF is so much faster on GPUs that it's a waste of a CPU to do TF in prime95.
If the exponent is so large (>2³²) that a GPU app such as mfakto or mfaktx can't be used, it's also further beyond prime95's capabilities.
From prime95's "whatsnew.txt":

Prime95 should not be used for trial factoring. GPUs are over 10 times more efficient at that task.

Some newer GPUs are up to ~5 bits (~40 times) more effective at TF than at P-1 or PRP.
These and much more are covered in the reference info collection.