diff --git a/src/fmpz_mod_mpoly/test/t-compose_fmpz_mod_mpoly.c b/src/fmpz_mod_mpoly/test/t-compose_fmpz_mod_mpoly.c
index 4cc93d9b2c..ce8414f643 100644
--- a/src/fmpz_mod_mpoly/test/t-compose_fmpz_mod_mpoly.c
+++ b/src/fmpz_mod_mpoly/test/t-compose_fmpz_mod_mpoly.c
@@ -25,7 +25,8 @@ TEST_FUNCTION_START(fmpz_mod_mpoly_compose, state)
         fmpz_mod_mpoly_ctx_t ctxAC, ctxB;
         slong * c;
 
-        fmpz_init_set_ui(p, 13);
+        fmpz_init(p);
+        fmpz_randprime(p, state, n_randint(state, 15) + 2, 0);
         fmpz_mod_mpoly_ctx_init(ctxB, nvarsB, ORD_LEX, p);
         fmpz_mod_mpoly_ctx_init(ctxAC, nvarsAC, ORD_LEX, p);
 
@@ -132,7 +133,8 @@ TEST_FUNCTION_START(fmpz_mod_mpoly_compose, state)
         slong len;
         flint_bitcnt_t exp_bits;
 
-        fmpz_init_set_ui(p, 13);
+        fmpz_init(p);
+        fmpz_randprime(p, state, n_randint(state, 15) + 2, 0);
         fmpz_mod_mpoly_ctx_init_rand(ctxB, state, 20, p);
         fmpz_mod_mpoly_ctx_init_rand(ctxAC, state, 20, p);
 
@@ -217,7 +219,8 @@ TEST_FUNCTION_START(fmpz_mod_mpoly_compose, state)
         fmpz_mod_mpoly_t f, g, g1, g2;
         fmpz_mod_mpoly_ctx_t ctx;
 
-        fmpz_init_set_ui(p, 13);
+        fmpz_init(p);
+        fmpz_randprime(p, state, n_randint(state, 15) + 2, 0);
         fmpz_mod_mpoly_ctx_init_rand(ctx, state, 10, p);
 
         vals1 = (fmpz_mod_mpoly_struct **) flint_malloc(ctx->minfo->nvars*
@@ -280,7 +283,8 @@ TEST_FUNCTION_START(fmpz_mod_mpoly_compose, state)
         slong len1, len2;
         slong exp_bound1, exp_bound2;
 
-        fmpz_init_set_ui(p, 13);
+        fmpz_init(p);
+        fmpz_randprime(p, state, n_randint(state, 15) + 2, 0);
         fmpz_mod_mpoly_ctx_init_rand(ctx1, state, 6, p);
         fmpz_mod_mpoly_ctx_init_rand(ctx2, state, 6, p);
 
diff --git a/src/nmod_mpoly/test/t-compose_nmod_mpoly.c b/src/nmod_mpoly/test/t-compose_nmod_mpoly.c
index eb01ae66b8..e56d175b30 100644
--- a/src/nmod_mpoly/test/t-compose_nmod_mpoly.c
+++ b/src/nmod_mpoly/test/t-compose_nmod_mpoly.c
@@ -24,9 +24,12 @@ TEST_FUNCTION_START(nmod_mpoly_compose_nmod_mpoly, state)
         nmod_mpoly_struct C[3];
         nmod_mpoly_ctx_t ctxAC, ctxB;
         slong * c;
+        ulong modulus;
 
-        nmod_mpoly_ctx_init(ctxB, nvarsB, ORD_LEX, 13);
-        nmod_mpoly_ctx_init(ctxAC, nvarsAC, ORD_LEX, 13);
+        modulus = n_randint(state, FLINT_BITS - 1) + 1;
+        modulus = n_randbits(state, modulus);
+        nmod_mpoly_ctx_init(ctxB, nvarsB, ORD_LEX, modulus);
+        nmod_mpoly_ctx_init(ctxAC, nvarsAC, ORD_LEX, modulus);
 
         nmod_mpoly_init(B, ctxB);
         nmod_mpoly_init(A, ctxAC);