diff --git a/journal/2024-07-12.md b/journal/2024-07-12.md
index c8eaa9d2c..a42265d15 100644
--- a/journal/2024-07-12.md
+++ b/journal/2024-07-12.md
@@ -14,4 +14,5 @@
 - Here I am having counted the primes up to 1000: [[168]]. So down to 16.8% of numbers being prime.
   - The [[Prime number theorem]] is what I was inching towards 
   - https://en.wikipedia.org/wiki/Prime-counting_function#Table_of_%CF%80(x),_x/log(x),_and_li(x) is a [[great table]]
-  - The ratio is roughly (x/log(x))
+  - The ratio of primes below number n which is exactly 1/#primes_below, can be estimated by 1/(x/log(x))
+  - Wow, had I never heard of [[logarithmic integral function]] before?
diff --git a/logarithmic integral function.md b/logarithmic integral function.md
new file mode 100644
index 000000000..c1e8a7b5e
--- /dev/null
+++ b/logarithmic integral function.md	
@@ -0,0 +1,2 @@
+- #go https://en.wikipedia.org/wiki/Logarithmic_integral_function
+- #pull related to the [[prime counting function]]