5 files changed, 57 insertions, 54 deletions

diff --git a/factors/factorize.go b/factors/factorize.go
index 8e82b16..9aa43a7 100644
--- a/factors/factorize.go
+++ b/factors/factorize.go
@@ -10,18 +10,20 @@ func Factors(n uint) []uint {
 	primeFactorization := PrimeFactorize(n)
 
 	factors := []uint{1}
-	for p, e := range primeFactorization.exponents {
-		next_factors := make([]uint, 0, len(factors)*int(e))
-		for _, factor := range factors {
-			for i := uint(0); i <= e; i++ {
-				multiplier := uint(1)
-				for j := uint(0); j < i; j++ {
-					multiplier *= p
-				}
-				next_factors = append(next_factors, factor*multiplier)
-			}
-		}
-		factors = next_factors
+	for prime, exponent := range primeFactorization.exponents {
+		factors = expandFactors(factors, prime, exponent)
 	}
 	return factors
 }
+
+// expandFactors takes a slice and returns a new slice where every factor
+// f in the original slice is replaced with f, f*p, f*p^2, ..., f*p^e.
+func expandFactors(factors []uint, prime, exponent uint) []uint {
+	nextFactors := make([]uint, 0, len(factors)*int(exponent))
+	for _, factor := range factors {
+		for i := uint(0); i <= exponent; i++ {
+			nextFactors = append(nextFactors, factor*uintpow(prime, i))
+		}
+	}
+	return nextFactors
+}
diff --git a/factors/prime_factorization.go b/factors/prime_factorization.go
index f91a2cf..d9f11e5 100644
--- a/factors/prime_factorization.go
+++ b/factors/prime_factorization.go
@@ -19,17 +19,13 @@ func PrimeFactorize(n uint) PrimeFactorization {
 		return PrimeFactorization{map[uint]uint{0: 1}}
 	}
 
-	unfactored := n // number with all found factors removed (divided)
+	unfactored := n
 	exponents := make(map[uint]uint)
 
-	// try each factor starting at 2
-	// if unfactored is divisible divide out until it isn't
-	for f := uint(2); f*f <= unfactored; {
-		if unfactored%f == 0 {
-			unfactored /= f
-			exponents[f] += 1
-		} else {
-			f += 1
+	for possibleFactor := uint(2); possibleFactor*possibleFactor <= unfactored; possibleFactor++ {
+		for unfactored%possibleFactor == 0 {
+			unfactored /= possibleFactor
+			exponents[possibleFactor] += 1
 		}
 	}
 
@@ -90,3 +86,7 @@ func (factors PrimeFactorization) String() string {
 	}
 	return strings.Join(parts, " × ")
 }
+
+func isPrime(p uint) bool {
+	return p > 1 && PrimeFactorize(p).Exponent(p) == 1
+}
diff --git a/factors/score.go b/factors/score.go
index 9288e8f..0759a74 100644
--- a/factors/score.go
+++ b/factors/score.go
@@ -36,26 +36,20 @@ func Score(n uint) float64 {
 // Also known as 2345 Rank.
 func BasicRank(n uint) string {
 	var firstRank, secondRank string
-	if n%2 == 0 {
-		if n%3 == 0 {
-			if n%4 == 0 {
-				firstRank = "A"
-			} else {
-				firstRank = "B"
-			}
-		} else {
-			if n%4 == 0 {
-				firstRank = "C"
-			} else {
-				firstRank = "D"
-			}
-		}
-	} else {
-		if n%3 == 0 {
-			firstRank = "E"
-		} else {
-			firstRank = "F"
-		}
+
+	switch uint(0) {
+	case n % 12:
+		firstRank = "A"
+	case n % 6:
+		firstRank = "B"
+	case n % 4:
+		firstRank = "C"
+	case n % 2:
+		firstRank = "D"
+	case n % 3:
+		firstRank = "E"
+	default:
+		firstRank = "F"
 	}
 
 	switch n % 5 {
diff --git a/factors/type.go b/factors/type.go
index 7a0f877..b58d01c 100644
--- a/factors/type.go
+++ b/factors/type.go
@@ -76,6 +76,15 @@ func Type(n uint) NumberType {
 	}
 }
 
+// invariant: p must be odd and >= 3
+func nextPrime(p uint) uint {
+	possiblePrime := p + 2
+	for !isPrime(possiblePrime) {
+		possiblePrime += 2
+	}
+	return possiblePrime
+}
+
 func exponentsOrdered(n uint) bool {
 	if n <= 2 {
 		return true
@@ -83,19 +92,17 @@ func exponentsOrdered(n uint) bool {
 		return false
 	}
 
-	pf := PrimeFactorize(uint(n))
+	pf := PrimeFactorize(n)
 	maxPrime := slices.Max(pf.Primes())
 
-	lastPrime := uint(2)
-	for p := uint(3); p <= maxPrime; p += 2 {
-		if PrimeFactorize(p).Exponent(p) == 1 {
-			if pf.Exponent(p) > pf.Exponent(lastPrime) {
-				return false
-			} else if pf.Exponent(p) == 0 && p < maxPrime {
-				return false
-			}
-			lastPrime = p
+	for prime, prevPrime := uint(3), uint(2); prime <= maxPrime; {
+		if pf.Exponent(prime) > pf.Exponent(prevPrime) {
+			return false
+		} else if pf.Exponent(prime) == 0 && prime < maxPrime {
+			return false
 		}
+
+		prime, prevPrime = nextPrime(prime), prime
 	}
 
 	return true
diff --git a/factors/uintpow.go b/factors/uintpow.go
index 85db67f..50bfe9d 100644
--- a/factors/uintpow.go
+++ b/factors/uintpow.go
@@ -1,9 +1,9 @@
 package factors
 
-func uintpow(a, b uint) uint {
+func uintpow(base, exponent uint) uint {
 	result := uint(1)
-	for i := uint(0); i < b; i++ {
-		result *= a
+	for i := uint(0); i < exponent; i++ {
+		result *= base
 	}
 	return result
 }