Results of testing Carmichael numbers to 10^24 (latest cubic test)

That is a strikingly clean outcome.
For the record:
[
\boxed{\min_{N<10^{24}\atop N\ \mathrm{Carmichael}}E_q(N)
=1.354882088024269\ldots}
]
under our least-admissible-(q) rule, attained at
[
N=739243849201,\qquad
\rho=\frac1{12045030055140096}.
]
Consequences of this census:
* The old record survives all (308{,}279{,}939) Carmichael numbers below (10^{24}).
* No entry has (E<1.35), (E<1), or (E=0).
* Hence there is no nuclear example in this table.
* Only 113 entries have (E<3/2).
* Only four have (E<1.4).
* The third-lowest value,
  [
  E=1.3741769148\ldots,
  ]
  occurs much later, at (N\approx5.4\times10^{22}), but does not seriously challenge the record.
* Inputs more than (10^{12}) times larger than the minimizer fail to improve it.
The preserved result is identified by:
```text
e42a490c0ebd4606e875514c679329ae68055e252f81a2c360e7fa7f2da5eea5
```
The next analysis should attach the supplied factorizations and (\omega(N)) to these 113 hits. This command streams through the table once:
```bash
awk 'NR==FNR{r[$1]=$2;e[$1]=$3;next}($1 in r){printf "%s %s %s %d",$1,r[$1],e[$1],NF-1;for(i=2;i<=NF;i++)printf " %s",$i;printf "\n"}' ~/abf_carmichael_E_lt_1p5.txt /mnt/c/Users/berni/Downloads/new_table.txt > ~/abf_carmichael_E_lt_1p5_factored.txt
```
Then verify:
```bash
wc -l ~/abf_carmichael_E_lt_1p5_factored.txt
sha256sum ~/abf_carmichael_E_lt_1p5_factored.txt
```
This is strong finite evidence for (E>1), with a substantial observed margin of (0.354882\ldots), but correctly remains a computational census rather than a proof beyond (10^{24}).