diff --git a/sage/gen_exhaustive_groups.sage b/sage/gen_exhaustive_groups.sage
index d2cad981a6..7553522432 100644
--- a/sage/gen_exhaustive_groups.sage
+++ b/sage/gen_exhaustive_groups.sage
@@ -72,10 +72,7 @@ def output_generator(g, name):
     print(")")
 
 def output_b(b):
-    print("static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(")
-    print("    0x%08x, 0x%08x, 0x%08x, 0x%08x," % tuple((int(b) >> (32 * (7 - i))) & 0xffffffff for i in range(4)))
-    print("    0x%08x, 0x%08x, 0x%08x, 0x%08x" % tuple((int(b) >> (32 * (7 - i))) & 0xffffffff for i in range(4, 8)))
-    print(");")
+    print(f"#  define SECP256K1_B {int(b)}")
 
 print()
 print()
@@ -104,7 +101,6 @@ for f in sorted(gens.keys()):
     print(f"#  {'if' if first else 'elif'} EXHAUSTIVE_TEST_ORDER == {f}")
     first = False
     print(f"static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G_ORDER_{f};")
-    print("")
     output_b(b)
 print("#  else")
 print("#    error No known generator for the specified exhaustive test group order.")
@@ -112,7 +108,6 @@ print("#  endif")
 print("#else")
 print()
 print("static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G;")
-print("")
 output_b(7)
 print()
 print("#endif")
diff --git a/src/group_impl.h b/src/group_impl.h
index 32e17590cd..8dff5bbb1a 100644
--- a/src/group_impl.h
+++ b/src/group_impl.h
@@ -42,33 +42,23 @@
 #if defined(EXHAUSTIVE_TEST_ORDER)
 #  if EXHAUSTIVE_TEST_ORDER == 13
 static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G_ORDER_13;
-
-static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(
-    0x00000000, 0x00000000, 0x00000000, 0x00000000,
-    0x00000000, 0x00000000, 0x00000000, 0x00000002
-);
+#  define SECP256K1_B 2
 #  elif EXHAUSTIVE_TEST_ORDER == 199
 static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G_ORDER_199;
-
-static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(
-    0x00000000, 0x00000000, 0x00000000, 0x00000000,
-    0x00000000, 0x00000000, 0x00000000, 0x00000004
-);
+#  define SECP256K1_B 4
 #  else
 #    error No known generator for the specified exhaustive test group order.
 #  endif
 #else
 
 static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G;
-
-static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(
-    0x00000000, 0x00000000, 0x00000000, 0x00000000,
-    0x00000000, 0x00000000, 0x00000000, 0x00000007
-);
+#  define SECP256K1_B 7
 
 #endif
 /* End of section generated by sage/gen_exhaustive_groups.size. */
 
+static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, SECP256K1_B);
+
 static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
     secp256k1_fe zi2;
     secp256k1_fe zi3;