# How to quickly find the last superior highly composite number smaller than a given number?

More specifically I want to find the last superior highly composite number less or equal to $$10^{12}$$.

I want to do this because I want to know which number has the most divisors and is less or equal to $$10^{12}$$.

Here is an article about such numbers

Added from the list of highly composite numbers, https://oeis.org/A002182/b002182.txt . Number 95: is the one you want

      321,253,732,800 =  2^6 3^3 5^2 7 11 13 17 19 23  log base ten  11.5068

95:   963,761,198,400 =  2^6 3^4 5^2 7 11 13 17 19 23
96: 1,124,388,064,800 =  2^5 3^3 5^2 7^2 11 13 17 19 23

2,248,776,129,600 =  2^6 3^3 5^2 7^2 11 13 17 19 23  log  ten  12.3519


If that is all you want

  log base ten  0.30103  2 =  2  log base ten  0.30103
4  log base ten  0.60206  6 =  2 3  log base ten  0.778151
6  log base ten  0.778151  12 =  2^2 3  log base ten  1.07918
12  log base ten  1.07918  60 =  2^2 3 5  log base ten  1.77815
16  log base ten  1.20412  120 =  2^3 3 5  log base ten  2.07918
24  log base ten  1.38021  360 =  2^3 3^2 5  log base ten  2.5563
48  log base ten  1.68124  2520 =  2^3 3^2 5 7  log base ten  3.4014
60  log base ten  1.77815  5040 =  2^4 3^2 5 7  log base ten  3.70243
120  log base ten  2.07918  55440 =  2^4 3^2 5 7 11  log base ten  4.74382
240  log base ten  2.38021  720720 =  2^4 3^2 5 7 11 13  log base ten  5.85777
288  log base ten  2.45939  1441440 =  2^5 3^2 5 7 11 13  log base ten  6.1588
384  log base ten  2.58433  4324320 =  2^5 3^3 5 7 11 13  log base ten  6.63592
576  log base ten  2.76042  21621600 =  2^5 3^3 5^2 7 11 13  log base ten  7.33489
1152  log base ten  3.06145  367567200 =  2^5 3^3 5^2 7 11 13 17  log base ten  8.56534
2304  log base ten  3.36248  6983776800 =  2^5 3^3 5^2 7 11 13 17 19  log base ten  9.84409
2688  log base ten  3.42943  13967553600 =  2^6 3^3 5^2 7 11 13 17 19  log base ten  10.1451
5376  log base ten  3.73046  321253732800 =  2^6 3^3 5^2 7 11 13 17 19 23  log base ten  11.5068
8064  log base ten  3.90655  2248776129600 =  2^6 3^3 5^2 7^2 11 13 17 19 23  log base ten  12.3519
16128  log base ten  4.20758  65214507758400 =  2^6 3^3 5^2 7^2 11 13 17 19 23 29  log base ten  13.8143
20160  log base ten  4.30449  195643523275200 =  2^6 3^4 5^2 7^2 11 13 17 19 23 29  log base ten  14.2915
40320  log base ten  4.60552  6064949221531200 =  2^6 3^4 5^2 7^2 11 13 17 19 23 29 31  log base ten  15.7828