Termination w.r.t. Q of the given QTRS could be proven:

(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

prime(0) → false
prime(s(0)) → false
prime(s(s(x))) → prime1(s(s(x)), s(x))
prime1(x, 0) → false
prime1(x, s(0)) → true
prime1(x, s(s(y))) → and(not(divp(s(s(y)), x)), prime1(x, s(y)))
divp(x, y) → =(rem(x, y), 0)

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Lexicographic path order with status [LPO].
Precedence:

prime₁ > s₁ > prime1₂ > true > false
prime₁ > s₁ > prime1₂ > and₂ > false
prime₁ > s₁ > prime1₂ > not₁ > false
prime₁ > s₁ > prime1₂ > divp₂ > 0 > false
prime₁ > s₁ > prime1₂ > divp₂ > =₂ > false
prime₁ > s₁ > prime1₂ > divp₂ > rem₂ > false

Status:

prime₁: [1]
0: []
false: []
s₁: [1]
prime1₂: [1,2]
true: []
and₂: [1,2]
not₁: [1]
divp₂: [1,2]
=₂: [1,2]
rem₂: [1,2]

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

prime(0) → false
prime(s(0)) → false
prime(s(s(x))) → prime1(s(s(x)), s(x))
prime1(x, 0) → false
prime1(x, s(0)) → true
prime1(x, s(s(y))) → and(not(divp(s(s(y)), x)), prime1(x, s(y)))
divp(x, y) → =(rem(x, y), 0)

(2) Obligation:

Q restricted rewrite system:
R is empty.
Q is empty.

(3) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(4) TRUE