diff --git a/safe_prime_generator.go b/safe_prime_generator.go
index e1a7799..7e87275 100644
--- a/safe_prime_generator.go
+++ b/safe_prime_generator.go
@@ -10,7 +10,6 @@ package paillier
 
 import (
 	"context"
-	"crypto/rand"
 	"errors"
 	"fmt"
 	"io"
@@ -63,6 +62,7 @@ func GenerateSafePrime(
 	bitLen int,
 	concurrencyLevel int,
 	timeout time.Duration,
+	random io.Reader,
 ) (p *big.Int, q *big.Int, err error) {
 	if bitLen < 6 {
 		return nil, nil, errors.New("safe prime size must be at least 6 bits")
@@ -82,7 +82,7 @@ func GenerateSafePrime(
 
 	for i := 0; i < concurrencyLevel; i++ {
 		runGenPrimeRoutine(
-			ctx, primeChan, errChan, mutex, waitGroup, rand.Reader, bitLen,
+			ctx, primeChan, errChan, mutex, waitGroup, random, bitLen,
 		)
 	}
 
diff --git a/safe_prime_generator_test.go b/safe_prime_generator_test.go
index b4e58a5..4b57efe 100644
--- a/safe_prime_generator_test.go
+++ b/safe_prime_generator_test.go
@@ -1,8 +1,8 @@
 package paillier
 
 import (
+	"crypto/rand"
 	"errors"
-	"math/big"
 	"reflect"
 	"testing"
 	"time"
@@ -44,6 +44,7 @@ func TestAsyncGenerator(t *testing.T) {
 				test.bitLen,
 				concurrencyLevel,
 				test.timeout,
+				rand.Reader,
 			)
 
 			if test.expectedError != nil {
@@ -59,38 +60,7 @@ func TestAsyncGenerator(t *testing.T) {
 					t.Fatal(err)
 				}
 
-				if !p.ProbablyPrime(20) {
-					t.Errorf("p is not prime; p = %v", p)
-				}
-
-				if !q.ProbablyPrime(20) {
-					t.Errorf("q is not prime; q = %v", q)
-				}
-
-				// p = 2q + 1 ?
-				expectedP := new(big.Int)
-				expectedP.Mul(big.NewInt(2), q)
-				expectedP.Add(expectedP, big.NewInt(1))
-
-				if expectedP.Cmp(p) != 0 {
-					t.Errorf("2q + 1 != p")
-				}
-
-				if p.BitLen() != test.bitLen {
-					t.Fatalf(
-						"Unexpected p bit length\nActual: %v\nExpected: %v",
-						p.BitLen(),
-						test.bitLen,
-					)
-				}
-
-				if q.BitLen() != test.bitLen-1 {
-					t.Fatalf(
-						"Unexpected q bit length\nActual: %v\nExpected: %v",
-						q.BitLen(),
-						test.bitLen-1,
-					)
-				}
+				AreSafePrimes(p, q, test.bitLen, t)
 			}
 		})
 	}
diff --git a/thresholdkey_generator.go b/thresholdkey_generator.go
index 1dab199..755745d 100644
--- a/thresholdkey_generator.go
+++ b/thresholdkey_generator.go
@@ -4,6 +4,7 @@ import (
 	"crypto/rand"
 	"io"
 	"math/big"
+	"time"
 )
 
 // Generates a threshold Paillier key with an algorithm based on [DJN 10],
@@ -58,7 +59,7 @@ func GetThresholdKeyGenerator(nbits, TotalNumberOfDecryptionServers, Threshold i
 }
 
 func (tkg *ThresholdKeyGenerator) generateSafePrimes() (*big.Int, *big.Int, error) {
-	return GenerateSafePrimes(tkg.nbits, tkg.Random)
+	return GenerateSafePrime(tkg.nbits, 4, 120*time.Second, tkg.Random)
 }
 
 func (tkg *ThresholdKeyGenerator) initPandP1() error {
diff --git a/utils.go b/utils.go
index 23944d4..98cca45 100644
--- a/utils.go
+++ b/utils.go
@@ -4,7 +4,6 @@ import (
 	"crypto/rand"
 	"io"
 	"math/big"
-	"time"
 )
 
 var ZERO = big.NewInt(0)
@@ -21,15 +20,6 @@ func Factorial(n int) *big.Int {
 	return ret
 }
 
-//  Returns 2 primes such that p = 2 * q + 1 and that the length of
-//  p is nbits.  `p` is called a safe prime
-//
-// Deprecated: This function has been left here just for backward compatibility.
-// Please use `GenerateSafePrime` from the `safe_prime_generator.go` directly.
-func GenerateSafePrimes(nbits int, random io.Reader) (p, q *big.Int, err error) {
-	return GenerateSafePrime(nbits, 4, 120*time.Second)
-}
-
 // Generate a random element in the group of all the elements in Z/nZ that
 // has a multiplicative inverse.
 func GetRandomNumberInMultiplicativeGroup(n *big.Int, random io.Reader) (*big.Int, error) {
diff --git a/utils_test.go b/utils_test.go
index 759e21a..cd86b9b 100644
--- a/utils_test.go
+++ b/utils_test.go
@@ -87,16 +87,6 @@ func GetEntireRQn(n int) map[int]bool {
 	return ret
 }
 
-func TestGenerateSafePrimes(t *testing.T) {
-	for i := 0; i < 10; i++ {
-		p, q, err := GenerateSafePrimes(20, rand.Reader)
-		if err != nil {
-			t.Error(err)
-		}
-		AreSafePrimes(p, q, 20, t)
-	}
-}
-
 func TestGetRandomGeneratorOfTheQuadraticResidue(t *testing.T) {
 	tooSmallPrime1, tooSmallPrime2 := b(347), b(359)
 	m := new(big.Int).Mul(tooSmallPrime1, tooSmallPrime2)