Factoring database
 |
|
|---|---|
| Factor database | |
| languages | English |
| operator | Markus Tervooren |
| editorial staff | all participants |
| Registration | optional |
| On-line | December 15, 2008 |
| http://www.factordb.com/ | |
The factoring database (also called factor database or factorDB for short ) is a database for factors with a web interface to search for factors and to report factors, which is operated by Markus Tervooren . While in other projects factors of numbers of a certain form are searched for, any natural numbers up to a certain limit are included in the database.
history
On December 11, 2008, Markus Tervooren decided to create such a database. He asked in the Mersenne forum of the Great Internet Mersenne Prime Search whether something like this already existed, and since nothing was known, he began to program the database. When it was completed on December 15, 2008, it was available at www.factorization.ath.cx/. Many improvements followed. Today the site is also available at http://www.factordb.com/.
Parts
The page is divided into seven parts:
Search ( search )
The search supports the following operators :
| operator | description | example |
|---|---|---|
| + | addition | 15 + 29 |
| - | subtraction | 221-21 |
| * | multiplication | 25 * 2 + 15 |
| / | division | 55/5 + 2 |
| % | Modulo | 33% 12 |
| ^ | Exponentiation | 25 * 2 ^ 1234 + 1 |
| ! | Faculty | 55! +1 |
| # | Product of all prime numbers under n ( Postfix ) | 123 # + 1 |
| ## | Product of the first n prime numbers ( Postfix ) | 44 ## + 1 |
| M. | Mersenne number ( prefix ) | M1061 |
| F. | Fermat number ( prefix ) | F12 |
| I. | Fibonacci number ( prefix ) | I123 |
| L. | Lucas number ( prefix ) | L662 |
When using variables (b, d, k, n, x, y and z are accepted as such) a factor table is created. For example, a factor table for Mersenne numbers can be generated by entering “Mn”.
Sequences ( sequences )
It can impact generated. These include aliquot sequences .
Results report ( report results )
In this section, factors can be reported and prime number certificates can be uploaded from PRIMO . A program from Dana Jacobsen is used to check the PRIMO certificates.
Factors are accepted in these formats:
- one factor per line, base 2/8/10 (with support of terms) / 16
- several factors per line, base 2/8/10/16
- GMP ECM edition
- Msieve edition
- Yafu edition
The prime number certificates can also be compressed into a ZIP file; the maximum size is around 200 megabytes .
Tables factors ( factor tables )
Examples of factor tables are presented in this section.
status
All information about the database can be found here:
- Workers
- statistics
- Prime numbers (over 110,000,000)
- PRP numbers (English probable prime , probable prime numbers) (over 58,000)
- Composite numbers with known factors (over 646,000,000)
- Composite numbers with no known factors (over 46,000,000)
- Numbers with the status "unknown" (over 40,000,000)
- Total (over 845,000,000)
- Smallest numbers with a certain property
- Least probable prime number
- Smallest composite number with no known factors
- Smallest number with the status "unknown"
- Interesting numbers
- Probable prime numbers according to the Miller-Rabin test , which later turned out to be composite (over 19,000; see also pseudoprime )
- Prime proofs
- N-1 method (over 552,000)
- N + 1 method (over 90,000)
- Combined N-1 / N + 1 method (39)
- Certificates (over 593,000)
- Probable prime / composite number distribution
- Tool: calculate group order
- Tool: Calculate the nearest prime over n
Downloads
This section can be used to download input files for PRIMO as a ZIP file, the list of all probable prime numbers in the database and 1,000 randomly selected small composite numbers.
Login ( login )
You can log in and register here. The login and display name and password are required for registration. The password is saved as an MD5 sum, which is unsafe.
Structure and storage of an entry
Each number is assigned an ID. The first 999 999 999 999 999 999 numbers contain themselves as ID. The IDs for numbers in the factor tables start with 1000000000000000000, all others with 1100000000000000001.
The entries are structured as follows:
status
A distinction is made between seven statuses:
- C - composite, no factors known: The number is a composite and no factors are known.
- CF - composite, (some) factors known: The number is a composite and some factors are known.
- FF - fully factored: The number is fully factored.
- P - (definitely) prime: The number is (definitely) prime.
- PRP - probably prime: The number is probably prime.
- U - unknown: It is unknown whether the number is composite, prime or probably prime.
- Unit: The number is a unit (only for the 1).
Numbers that were recently added to the database are marked with a red asterisk .
Filters ( digits )
The number of digits is indicated; the number can be converted into other place value systems (from base 2 to 36).
Number ( number )
The number is shown, possibly shortened.
Worker ( workers )
Workers are computers that do a specific job in the database.
Loopholes and (fixed) errors
The old user page has been removed and a new one is under development. The Perl script that everyone could use to log in as workers has also been abolished.
With the “set prime” button, which made it possible to classify numbers as prime without proof, many errors were found, which is why it was removed.