From c3f898531a1a9cf8b1078a70ef7ddfabc4eb6cf8 Mon Sep 17 00:00:00 2001
From: Gloria Mundi <gloria@gloria-mundi.eu>
Date: Wed, 5 Jun 2024 20:04:08 +0200
Subject: remove divisors of highly composite numbers, add primes below each
 power of 10

---
 math/tables/prime-composite.tex | 42 ++++++++++++++++++++---------------------
 1 file changed, 21 insertions(+), 21 deletions(-)

(limited to 'math/tables/prime-composite.tex')

diff --git a/math/tables/prime-composite.tex b/math/tables/prime-composite.tex
index d969747..d2b02e5 100644
--- a/math/tables/prime-composite.tex
+++ b/math/tables/prime-composite.tex
@@ -1,26 +1,26 @@
-\begin{tabularx}{\linewidth}{|r|r|r|r|CICICICICICICICICICICIC|}
+\begin{tabularx}{\linewidth}{|R|R|R|RIR|}
 	\hline
-	\multicolumn{16}{|c|}{Primes and Highly Composite Numbers} \\
+	\multicolumn{5}{|c|}{Primes and Highly Composite Numbers} \\
 	\hline
-	$10^x$ & Next Prime & Highly Composite & Divisors & 2 & 3 & 5 & 7 & 11 & 13 & 17 & 19 & 23 & 29 & 31 & 37 \\
+	$10^x$ & Next Prime & Primes Below & Highly Composite & Divisors \\
 	\hline
-	1 & +1 & 6 & 4 & 1 & 1 & & & & & & & & & & \\
-	2 & +1 & 60 & 12 & 2 & 1 & 1 & & & & & & & & & \\
-	3 & +9 & 840 & 32 & 3 & 1 & 1 & 1 & & & & & & & &\\
-	4 & +7 & 7560 & 64 & 3 & 3 & 1 & 1 & & & & & & & & \\
-	5 & +3 & 83160 & 128 & 3 & 3 & 1 & 1 & 1 & & & & & & & \\
-	6 & +3 & 720720 & 240 & 4 & 2 & 1 & 1 & 1 & 1 & & & & & & \\
-	7 & +19 & 8648640 & 448 & 6 & 3 & 1 & 1 & 1 & 1 & & & & & & \\
-	8 & +7 & 73513440 & 768 & 5 & 3 & 1 & 1 & 1 & 1 & 1 & & & & & \\
-	9 & +7 & 735134400 & 1344 & 6 & 3 & 2 & 1 & 1 & 1 & 1 & & & & & \\
-	10 & +19 & 6983776800 & 2304 & 5 & 3 & 2 & 1 & 1 & 1 & 1 & 1 & & & & \\
-	11 & +3 & 97772875200 & 4032 & 6 & 3 & 2 & 2 & 1 & 1 & 1 & 1 & & & & \\
-	12 & +39 & 963761198400 & 6720 & 6 & 4 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & & & \\
-	13 & +37 & 9316358251200 & 10752 & 6 & 3 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & & \\
-	14 & +31 & 97821761637600 & 17280 & 5 & 4 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & & \\
-	15 & +37 & 866421317361600 & 26880 & 6 & 4 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & \\
-	16 & +61 & 8086598962041600 & 41472 & 8 & 3 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & \\
-	17 & +3 & 74801040398884800 & 64512 & 6 & 3 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\
-	18 & +3 & 897612484786617600 & 103680 & 8 & 4 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\
+	1 & +1 & 4 & 6 & 4 \\
+	2 & +1 & 25 & 60 & 12 \\
+	3 & +9 & 168 & 840 & 32 \\
+	4 & +7 & 1229 & 7560 & 64 \\
+	5 & +3 & 9592 & 83160 & 128 \\
+	6 & +3 & 78498 & 720720 & 240 \\
+	7 & +19 & 664579 & 8648640 & 448 \\
+	8 & +7 & 5761455 & 73513440 & 768 \\
+	9 & +7 & 50847534 & 735134400 & 1344 \\
+	10 & +19 & 455052511 & 6983776800 & 2304 \\
+	11 & +3 & 4118054813 & 97772875200 & 4032 \\
+	12 & +39 & \multirow{7}={$$\approx \frac{0.43 \cdot 10^x}{x}$$} & 963761198400 & 6720 \\
+	13 & +37 & & 9316358251200 & 10752 \\
+	14 & +31 & & 97821761637600 & 17280 \\
+	15 & +37 & & 866421317361600 & 26880 \\
+	16 & +61 & & 8086598962041600 & 41472 \\
+	17 & +3 & & 74801040398884800 & 64512 \\
+	18 & +3 & & 897612484786617600 & 103680 \\
 	\hline
 \end{tabularx}
-- 
cgit v1.2.3

