diff --git a/util/primes.go b/util/primes.go
new file mode 100644
index 0000000..8d04823
--- /dev/null
+++ b/util/primes.go
@@ -0,0 +1,34 @@
+package util
+
+import (
+	"math"
+)
+
+// GeneratePrimes returns the n-th prime number
+// its param primes []int is intended to contain previously found prime numbers
+// to reduce duplicated work, but still be testable
+func GeneratePrimes(primes []int, n int) int {
+	if len(primes) < 2 {
+		primes = []int{2, 3}
+	}
+	if len(primes) >= n {
+		return primes[n-1]
+	}
+	for i := primes[len(primes)-1] + 2; len(primes) <= n; i += 2 {
+		// check if i is a prime number by checking if it is divisible by any of the previous values of primes
+		// stop at the square root of i
+		for _, v := range primes {
+			// not a prime, stop this loop
+			if i%v == 0 {
+				break
+			}
+			if math.Sqrt(float64(i)) < float64(v) {
+				// add to primes
+				primes = append(primes, i)
+				break
+			}
+		}
+	}
+
+	return primes[n-1]
+}
diff --git a/util/primes_test.go b/util/primes_test.go
new file mode 100644
index 0000000..ae7f1ab
--- /dev/null
+++ b/util/primes_test.go
@@ -0,0 +1,52 @@
+package util
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestGeneratePrimes(t *testing.T) {
+	tests := []struct {
+		previousPrimes []int
+		n, expected    int
+	}{
+		{[]int{2, 3}, 1, 2},
+		{[]int{2, 3}, 2, 3},
+		{[]int{2, 3}, 3, 5},
+		{[]int{2, 3}, 4, 7},
+		{[]int{2, 3, 5, 7}, 4, 7},
+		{[]int{2, 3, 5, 7}, 5, 11},
+		{[]int{2, 3, 5, 7}, 6, 13},
+		{[]int{2, 3}, 7, 17},
+		{[]int{2, 3}, 8, 19},
+	}
+	for _, test := range tests {
+		t.Run(fmt.Sprintf("%v-th prime number", test.n),
+			func(t *testing.T) {
+				ans := GeneratePrimes(test.previousPrimes, test.n)
+				if ans != test.expected {
+					t.Errorf("Expected %v-th prime to be %v, got %v", test.n, test.expected, ans)
+				}
+			},
+		)
+	}
+}
+
+// run go test -bench=. from within this util folder
+// Benchmark
+func benchGenPrimes(n int, b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		GeneratePrimes([]int{2, 3}, n)
+	}
+}
+
+// Benchmark generating different magnitudes of primes...
+func BenchmarkGeneratePrimes10(b *testing.B)      { benchGenPrimes(10, b) }
+func BenchmarkGeneratePrimes100(b *testing.B)     { benchGenPrimes(100, b) }
+func BenchmarkGeneratePrimes1000(b *testing.B)    { benchGenPrimes(1000, b) }
+func BenchmarkGeneratePrimes10000(b *testing.B)   { benchGenPrimes(10000, b) }
+func BenchmarkGeneratePrimes100000(b *testing.B)  { benchGenPrimes(100000, b) }
+func BenchmarkGeneratePrimes1000000(b *testing.B) { benchGenPrimes(1000000, b) }
+
+// takes ~2 minutes on my mac
+// func BenchmarkGeneratePrimes10000000(b *testing.B) { benchGenPrimes(10000000, b) }