From ac766f4f6ab9db683e29b093bbc48cfe3b27b2b7 Mon Sep 17 00:00:00 2001
From: Adrien Hopkins <adrien.p.hopkins@gmail.com>
Date: Mon, 22 Sep 2025 15:56:30 -0500
Subject: Show regular complexity of prime factors

This metric shows how many combinations you'll need to memorize prime
powers, and how big the numbers are in complementary multiplication.

The YouTube video "the best way to count" inspired me to think I need
a metric to handle both size and factors, but the specific metric is
entirely original (or at least independently discovered).
---
 factor_info.go | 31 ++++++++++++++++++++++++++++++-
 1 file changed, 30 insertions(+), 1 deletion(-)

(limited to 'factor_info.go')

diff --git a/factor_info.go b/factor_info.go
index 637bde2..638e333 100644
--- a/factor_info.go
+++ b/factor_info.go
@@ -63,6 +63,11 @@ type factorInfo struct {
 	// reciprocoal has and what patterns are in its row of the multiplication
 	// table.
 	DigitMap []factors.DigitType
+	// The complexity of each prime factor.
+	// The amount of numbers to memorize for testing p^e is around RC(p)^e.
+	// The memorization for the product of prime powers
+	// is less than the memorization of worst part of the product.
+	PrimeRegularComplexities map[uint]float64
 }
 
 const (
@@ -108,10 +113,12 @@ func getFactorInfo(a args) *factorInfo {
 	totativeCount := factors.Totient(radix)
 	totativeRatio := float64(totativeCount) / float64(radix)
 
+	var prcs = factors.PrimeRegularComplexities(radix)
+
 	return &factorInfo{radix, factors.PrimeFactorize(radix),
 		r_factors, factors.Score(radix), totativeCount, totativeRatio,
 		totativeDigits, factors.BasicRank(radix), factors.Type(radix),
-		mtc_ptr, math.Log2(float64(radix)), digitMap}
+		mtc_ptr, math.Log2(float64(radix)), digitMap, prcs}
 }
 
 func (fi *factorInfo) writeTo(w io.Writer) {
@@ -141,6 +148,9 @@ func (fi *factorInfo) writeTo(w io.Writer) {
 	fmt.Fprintf(w, "Base-2 Logarithm: %.3f\n", fi.Log2)
 	fmt.Fprintf(w, "Number Length: %.4f×Decimal\n",
 		1/math.Log10(float64(fi.Radix)))
+	fmt.Fprint(w, "Prime Regular Complexities: ")
+	writePRCMap(w, fi.PrimeRegularComplexities)
+	fmt.Fprintln(w)
 	if len(fi.DigitMap) > 0 {
 		writeDigitMap(w, fi.DigitMap)
 	}
@@ -193,3 +203,22 @@ func typeAbbrev(t factors.CompositenessType) string {
 		panic("Should not be possible to get here.")
 	}
 }
+
+func writePRCMap(w io.Writer, prcs map[uint]float64) {
+	var first = true
+	var primeFactors = make([]uint, 0, len(prcs))
+	for p := range prcs {
+		primeFactors = append(primeFactors, p)
+	}
+	sort.Slice(primeFactors, func(i, j int) bool {
+		return primeFactors[i] < primeFactors[j]
+	})
+
+	for _, p := range primeFactors {
+		if !first {
+			fmt.Fprintf(w, ", ")
+		}
+		first = false
+		fmt.Fprintf(w, "%d: %.4f", p, prcs[p])
+	}
+}
-- 
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