diff --git a/src/crypto/rand/util.go b/src/crypto/rand/util.go
index 4dd1711203..0f143a3830 100644
--- a/src/crypto/rand/util.go
+++ b/src/crypto/rand/util.go
@@ -10,28 +10,11 @@ import (
 	"math/big"
 )
 
-// smallPrimes is a list of small, prime numbers that allows us to rapidly
-// exclude some fraction of composite candidates when searching for a random
-// prime. This list is truncated at the point where smallPrimesProduct exceeds
-// a uint64. It does not include two because we ensure that the candidates are
-// odd by construction.
-var smallPrimes = []uint8{
-	3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
-}
-
-// smallPrimesProduct is the product of the values in smallPrimes and allows us
-// to reduce a candidate prime by this number and then determine whether it's
-// coprime to all the elements of smallPrimes without further big.Int
-// operations.
-var smallPrimesProduct = new(big.Int).SetUint64(16294579238595022365)
-
-// Prime returns a number, p, of the given size, such that p is prime
-// with high probability.
+// Prime returns a number of the given bit length that is prime with high probability.
 // Prime will return error for any error returned by rand.Read or if bits < 2.
-func Prime(rand io.Reader, bits int) (p *big.Int, err error) {
+func Prime(rand io.Reader, bits int) (*big.Int, error) {
 	if bits < 2 {
-		err = errors.New("crypto/rand: prime size must be at least 2-bit")
-		return
+		return nil, errors.New("crypto/rand: prime size must be at least 2-bit")
 	}
 
 	b := uint(bits % 8)
@@ -40,13 +23,10 @@ func Prime(rand io.Reader, bits int) (p *big.Int, err error) {
 	}
 
 	bytes := make([]byte, (bits+7)/8)
-	p = new(big.Int)
-
-	bigMod := new(big.Int)
+	p := new(big.Int)
 
 	for {
-		_, err = io.ReadFull(rand, bytes)
-		if err != nil {
+		if _, err := io.ReadFull(rand, bytes); err != nil {
 			return nil, err
 		}
 
@@ -69,35 +49,8 @@ func Prime(rand io.Reader, bits int) (p *big.Int, err error) {
 		bytes[len(bytes)-1] |= 1
 
 		p.SetBytes(bytes)
-
-		// Calculate the value mod the product of smallPrimes. If it's
-		// a multiple of any of these primes we add two until it isn't.
-		// The probability of overflowing is minimal and can be ignored
-		// because we still perform Miller-Rabin tests on the result.
-		bigMod.Mod(p, smallPrimesProduct)
-		mod := bigMod.Uint64()
-
-	NextDelta:
-		for delta := uint64(0); delta < 1<<20; delta += 2 {
-			m := mod + delta
-			for _, prime := range smallPrimes {
-				if m%uint64(prime) == 0 && (bits > 6 || m != uint64(prime)) {
-					continue NextDelta
-				}
-			}
-
-			if delta > 0 {
-				bigMod.SetUint64(delta)
-				p.Add(p, bigMod)
-			}
-			break
-		}
-
-		// There is a tiny possibility that, by adding delta, we caused
-		// the number to be one bit too long. Thus we check BitLen
-		// here.
-		if p.ProbablyPrime(20) && p.BitLen() == bits {
-			return
+		if p.ProbablyPrime(20) {
+			return p, nil
 		}
 	}
 }