Package: primePy
primes from module primePyThis 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 startedDownload the file primes.py and place it in the same directory where your python is installed. Or, simply run the command>>>pip install primePyto install the package. After installing viapipyou can call it by>>>from primePy import primesand then execute the available methods.Available methodsYou may runprimes.about()afer importing the package. The following is a list of all included methods.primes.check(n)returnsTrueifnis a prime number.primes.factor(n)returns the lowest prime factor ofn.primes.facors(n)returns all the prime factors ofnwith multiplicity.primes.first(n)returns firstnmany prime.primes.upto(n)returns all the prime less than or equal ton.primes.between(m,n)returns all the prime betweenmandn.primes.phi(n)returns the Euler'sphi(n)i.e., the number of integers less thannwhich have no common factor withn.DemonstrationThis program is tested on my personal laptop with the following configurations.Processor: Intel(R) Core(TM) i3-4030U CPU @ 1.90GhzInstalled memory(RAM): 6.00GBSystem type: 64 bit Operating System, x64-based processorOperating system: Windows 10Small numbersAll the following commands returnd results in less than1 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)
483618287856960A little bigger numbersAll the following commands returned results in less than5 secs.>>> primes.factors(2910046587320501324077792713140104371205630933992706145011)
[239, 701, 709, 1997, 1997, 3889, 5171, 5171, 6983, 10009, 4940867, 45845791, 3731292319]>>> primes.first(10000)[9999]
104729The last command returns the 10000th prime.SuggestionsFeel free to drop your suggestion at the following email addressAuthor: Indrajit JanaEmail: ijana at temple dot edu