[ET_]

Originally Posted by rogue

The program I use to find the existing gaps (which are all reserved) also outputs a file that groups the n as follows:

    14 <= n <     100, each group has 1 n
   100 <= n <    1000, each group has 10 n from xx0 to xx9
  1000 <= n <   10000, each group has 100 n from xx00 to xx99
 10000 <= n <  100000, each group has 1000 n from xx000 to xx999

into a file called groups.txt. For each group it lists the max k that the group was tested to. You will notice that the file uses scientific notation to represent that k. This makes the data far more readable. Looking at the data implies that the size of the range of k should be a multiple of certain values determined by the n. For example:

• if n < 100, k should be a multiple of 1e14
• if 100 <= n < 399, k should be a multiple of 1e12
• if 400 <= n < 999, k should be a multiple of 1e11
• if 1000 <= n < 9999, k should be a multiple of 1e8
• if 10000 <= n < 39999, k should be a multiple of 1e6
• if 40000 <= n < 99999, k should be a multiple of 1e4

If you look at the groups.txt file in the attached zip file, you will see exactly how I came up with these numbers. Based upon this data I would add these to the "Most Wanted" ranges:

• n : 900-949 , k :180e to 200e9
• n : 950-999 , k :150e9 to 200e9
• n : 8000-8999 , k : 350e6 to 400e6
• n : 9000-9999 , k : 260e6 to 300e6
• n : 60000-61999 , k : 125e3 to 130e3

When I look at the file, I also see ranges like this:

n 4400-4499    maxk     2000e6
n 4500-4599    maxk      700e6
n 4600-4699    maxk      700e6
n 4700-4799    maxk      700e6
n 4800-4899    maxk      700e6
n 4900-4999    maxk      700e6
n 5000-5099    maxk     1200e6

Where subsequent ranges are tested to a higher k than previous ranges. I would add this to the "Most Wanted" ranges:

• n : 4500-4999 , k : 700e6 to 1200e6

If this is desirable information to mine from the FermatSearch pages, then I can modify the program to output these ranges in addition to the gaps.

I can provide you with a new table, where you can insert the most wanted ranges and I could peek from it to have the site updated instead of updating it manually.
Let's just discuss the details...