diff --git a/plonky2/examples/factorial.rs b/plonky2/examples/factorial.rs
new file mode 100644
index 00000000..6a2771f2
--- /dev/null
+++ b/plonky2/examples/factorial.rs
@@ -0,0 +1,36 @@
+use anyhow::Result;
+use plonky2::field::types::Field;
+use plonky2::iop::witness::PartialWitness;
+use plonky2::plonk::circuit_builder::CircuitBuilder;
+use plonky2::plonk::circuit_data::CircuitConfig;
+use plonky2::plonk::config::{GenericConfig, PoseidonGoldilocksConfig};
+
+fn main() -> Result<()> {
+    const D: usize = 2;
+    type C = PoseidonGoldilocksConfig;
+    type F = <C as GenericConfig<D>>::F;
+
+    let config = CircuitConfig::standard_recursion_config();
+
+    let pw = PartialWitness::new();
+    let mut builder = CircuitBuilder::<F, D>::new(config);
+
+    let mut cur_target = builder.one();
+    for i in 2..101 {
+        let i_target = builder.constant(F::from_canonical_u32(i));
+        cur_target = builder.mul(cur_target, i_target);
+    }
+
+    let fact_100 = F::from_canonical_u64(3822706312645553057);
+    let fact_100_target = builder.constant(fact_100);
+    builder.register_public_input(fact_100_target);
+
+    builder.connect(fact_100_target, cur_target);
+
+    let data = builder.build::<C>();
+    let proof = data.prove(pw)?;
+
+    println!("100 factorial (mod |F|) is: {}", proof.public_inputs[0]);
+
+    data.verify(proof)
+}
diff --git a/plonky2/examples/square_root.rs b/plonky2/examples/square_root.rs
new file mode 100644
index 00000000..3fce9030
--- /dev/null
+++ b/plonky2/examples/square_root.rs
@@ -0,0 +1,35 @@
+use anyhow::Result;
+use plonky2::field::types::Field;
+use plonky2::iop::witness::PartialWitness;
+use plonky2::plonk::circuit_builder::CircuitBuilder;
+use plonky2::plonk::circuit_data::CircuitConfig;
+use plonky2::plonk::config::{GenericConfig, PoseidonGoldilocksConfig};
+
+fn main() -> Result<()> {
+    const D: usize = 2;
+    type C = PoseidonGoldilocksConfig;
+    type F = <C as GenericConfig<D>>::F;
+
+    let config = CircuitConfig::standard_recursion_config();
+
+    let pw = PartialWitness::new();
+    let mut builder = CircuitBuilder::<F, D>::new(config);
+
+    let x = F::rand();
+    let x_squared = x * x;
+    let x_target = builder.constant(x);
+    let x_squared_target = builder.constant(x_squared);
+
+    let x_squared_computed = builder.mul(x_target, x_target);
+    builder.connect(x_squared_target, x_squared_computed);
+
+    builder.register_public_input(x_target);
+
+    let data = builder.build::<C>();
+    let proof = data.prove(pw)?;
+
+    println!("Random field element: {}", x_squared);
+    println!("Its square root: {}", proof.public_inputs[0]);
+
+    data.verify(proof)
+}