In early 2024, we audited the results for the factorizations to double-check corrupted backups. We found errors. From the ORIGINAL sub-totals, we found errors on file(s):
File # Correct Value:
001 2032 80222
004 1833 12229
007 1785 74138
015 1728 02161
090 1610 00490
113 1596 38520
114 1595 89620
134 1586 32383
135 1585 88179
and
199 1563 36388
It is possible, to work out what the corrected totals should be by working from the pictured documentation. Finding the greatest portion of the data to be correct, and by double checking those entries found to be questionable on a different machine, we at Indentured Geek now wish to certify these totals to be accurate and correct. We apologize for earlier inaccuracies.
In 2023, technical limitations (and the logarithmic progression of the degree of difficulty,) led us to delay factoring 120-digit numbers. If and when these become available, they will be accompanied by 20 runs of 500 sequential non-primes in the 5.1 x 10^20 range which we have already computed.
Instead, we computed a list of ALL Primes < 2^40. This amounts to 256 files of primes, each containing the primes of 2^32 (4.3 B_illion) values. Not all 4.3 B_illion numbers are prime in each range, but the distribution of primes was not available before. The tables below show them.
Mathematically, this is drudge work and is provided to further the investigations of educators and students. The entire database is over 540 GB of data.
Each individual file spans 4.29 billion numbers, and the counts list how many Primes were found within each range.
2^32 x
2^32 x 64 is 2^38th.
2^38 is 64 files, all told.
2^37th is the first half, taking 32 files.
The second half takes 32 files by itself.
2^32 x
2^32 x 128 is 2^39th.
2^39th is 64 more files!
2^32 x
2^32 x
2^32 x 256 is 2^40th.
Files from 2^39 to 2^40 comprise 128 more files, just for one order of magnitude.
2^32 x
These numbers may seem tedious, but there is no shortcut to investigating the distribution of Primes.
2^32 x
2^40th - 2^39th is 128 files all by itself!
Final sub-totals for 2^40th.
