This module contains several useful functions to work with prime numbers. from primePy import primes

# primes from module primePy

This module contains several useful functions to work with prime numbers. For example, extracting all the prime factors (with multiplicity) of a positive integer reasonably fast. Following the list of all functions and their running time.

## Getting started

Download the file primes.py and place it in the same directory where your python is installed. Or, simply run the command

>>>pip install primePy


to install the package. After installing via pip you can call it by

>>>from primePy import primes


and then execute the available methods.

## Available methods

You may run primes.about() afer importing the package. The following is a list of all included methods.

primes.check(n) returns True if n is a prime number.
primes.factor(n) returns the lowest prime factor of n.
primes.facors(n) returns all the prime factors of n with multiplicity.
primes.first(n) returns first n many prime.
primes.upto(n) returns all the prime less than or equal to n.
primes.between(m,n) returns all the prime between m and n.
primes.phi(n) returns the Euler's phi(n) i.e., the number of integers less than n which have no common factor with n.

## Demonstration

This program is tested on my personal laptop with the following configurations.

Processor: Intel(R) Core(TM) i3-4030U CPU @ 1.90Ghz
Installed memory(RAM): 6.00GB
System type: 64 bit Operating System, x64-based processor
Operating system: Windows 10

### Small numbers

All the following commands returnd results in less than 1 sec.

>>> primes.check(56156149)
False
>>> primes.check(79012338765433)
True

>>> primes.factor(7568945625)
3
>>> primes.factor(5141)
53

>>> primes.factors(252)
[2, 2, 3, 3, 7]
>>> primes.factors(44410608)
[2, 2, 2, 2, 3, 3, 11, 23, 23, 53]

>>> primes.first(7)
[2, 3, 5, 7, 11, 13, 17]
>>> primes.first(37)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157]
>>> primes.first(5000)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179,
. . . .
. . . .
48179, 48187, 48193, 48197, 48221, 48239, 48247, 48259, 48271, 48281, 48299, 48311, 48313, 48337, 48341, 48353, 48371, 48383, 48397, 48407, 48409, 48413, 48437, 48449, 48463, 48473, 48479, 48481, 48487, 48491, 48497, 48523, 48527, 48533, 48539, 48541, 48563, 48571, 48589, 48593, 48611]


Outcomes from the last command is truncated.

>>> primes.upto(16)
[2, 3, 5, 7, 11, 13]
>>> primes.upto(50000)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179
. . .
. . .
49789, 49801, 49807, 49811, 49823, 49831, 49843, 49853, 49871, 49877, 49891, 49919,
49921, 49927, 49937, 49939, 49943, 49957, 49991, 49993, 49999]

>>> primes.between(100,200)
[101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199]
>>> primes.between(100000,500000)
[100003, 100019, 100043, 100049, 100057, 100069, 100103, 100109, 100129, 100151, 100153,
100169, 100183, 100189, 100193, 100207, 100213, 100237, 100267, 100271, 100279, 100291

499661, 499663, 499669, 499673, 499679, 499687, 499691, 499693, 499711, 499717, 499729, 499739, 499747, 499781, 499787, 499801, 499819, 499853, 499879, 499883, 499897, 499903, 499927, 499943, 499957, 499969, 499973, 499979]

>>> primes.phi(128)
64
>>> primes.phi(561534567567457)
483618287856960


### A little bigger numbers

All the following commands returned results in less than 5 secs.

>>> primes.factors(2910046587320501324077792713140104371205630933992706145011)
[239, 701, 709, 1997, 1997, 3889, 5171, 5171, 6983, 10009, 4940867, 45845791, 3731292319]

>>> primes.first(10000)[9999]
104729


The last command returns the 10000th prime.

## Suggestions

Author: Indrajit Jana
Email: ijana at temple dot edu

## Project details

Uploaded Source
Uploaded Python 3