Prime-numbers

Some demo prime number methods using elementary pure Python.

Contains

primzahl.py: A CLI demo script to serve as a frontend for invoking prime number methods and displaying their results. These functions are prime factorization,looking up the next prime (twin) and counting primes and prime twins below a certain number. Whenever possible, just hitting ENTER uses last function's output as input. So for example, ENTER will continue to show primes (or prime twins respectively) in ascending order.
primes.py: Contains the class definition for all prime number calculations. Can be used independently from the other files. Loading stored, previously calculated prime numbers is done during import - not during object creation. The __del__ method of this class automatically performs a save to disk, if new prime numbers have been calculated. There is a built-in limit on the largest prime saved to disk, currently 5 million. This limit can be overwritten during object creation, and of course the definition can be updated, too. Prime numbers are stored as 32 bit integers ("unsigned long", using the array standard Python module, not a simple list), so there is an absolute upper limit of about 4.3 billion for the largest usable prime number. When new primes must be claculated, a deterministic version of the Miller-Rabin-Test is used.
primzahl.de, primzahl.es: optional files defining message translations from English to German and Spanish, respectively. The CLI script primzahl.py will check its first invocation parameter for an appropriate file extension - "de"and "es" in these cases. In order to support your favorite language, create a primzahl.xx file and invoke the script with the parameter xx. If missing, English will be used.
primenumbers.zip: an optional file containing prime numbers until about one million. To be placed in the user's home directory. The actual prime number data in this file is LZMA-compressed (Python 3, or DEFLATEd in Python 2) and only occupies 58 KB. Will be extended automatically, based on highest prime number used in a session. Will be created automatically in the user's home directory if missing. During a session, these data serve as a cache to keep calculations of new prime number to a minimum.

Features

Perform prime factorization of an integer. Returns a list of pairs [p, e], where p is a prime and e its exponent. Primes obviously only contain one such pair.
Return the smallest prime following a given number.
Return the smallest prime twin following a given number.
Return count of primes less or equal a given number (so-called Pi function).
Return count of prime twins less or equal a given number.
Automatically append new calculated prime numbers to an array.array of format "L" (unsigned long).
Automatically save the prime number array in a zip file, if new primes have been created in the current session.

Dependency Notes

Runs with Python 2 or 3.

When switching back from Python 3 to Python 2 an eventually existing primenumbers.zip file must be deleted first, because Python 2 does not support compression LZMA (which is automatically used if Python 3).

No issues exist, when switching from Python 2 to Python 3. The next prime number save under Python 3 will automatically use LZMA compression.

Changes

Use the deterministic version of the Miller-Rabin-Test for primality. This is about 30 - 50% more efficient than Eratosthenes in our context.
Use of binary search module bisect when looking up the index of a prime.
Parameterize message translations in the CLI script.

Example Session

Last prime number in store: 1001003 (78574 entries)
====== Prime number functions ======
     1: prime factors
     2: next prime number
     3: next prime twin
     4: count prime numbers
     5: count prime number twins
     q: quit
> 1
=== Find prime factors ===
Enter a number or 'q': 478523
Factors: [[478523, 1]]

Enter a number or 'q': 397397
Factors: [[7, 1], [11, 1], [13, 1], [397, 1]]

Enter a number or 'q': q
====== Prime number functions ======
     1: prime factors
     2: next prime number
     3: next prime twin
     4: count prime numbers
     5: count prime number twins
     q: quit
> 2
=== Find the next prime ===
ENTER, a number or 'q':
Next prime: 397427                    # ENTER was hit, so show prime >= 397397

ENTER, a number or 'q':
Next prime: 397429

ENTER, a number or 'q': q
====== Prime number functions ======
     1: prime factors
     2: next prime number
     3: next prime twin
     4: count prime numbers
     5: count prime number twins
     q: quit
> 3
=== Find the next prime twin ===
ENTER, a number or 'q': 999999
Next prime twin: (1000037, 1000039)

ENTER, a number or 'q': q
====== Prime number functions ======
     1: prime factors
     2: next prime number
     3: next prime twin
     4: count prime numbers
     5: count prime number twins
     q: quit
> 4
=== Count previous primes ===
Enter a number or 'q': 999999
78498
Enter a number or 'q': q
====== Prime number functions ======
     1: prime factors
     2: next prime number
     3: next prime twin
     4: count prime numbers
     5: count prime number twins
     q: quit
> 5
=== Count previous prime twins ===
Enter a number or 'q': 999999
8169
Enter a number or 'q': q
====== Prime number functions ======
     1: prime factors
     2: next prime number
     3: next prime twin
     4: count prime numbers
     5: count prime number twins
     q: quit
> q
$

JorjMcKie / Prime-numbers