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Unify the various versions of is_prime() #5642

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191 changes: 4 additions & 187 deletions ciphers/rabin_miller.py
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -2,6 +2,8 @@

import random

from maths.prime_check import prime_check


def rabinMiller(num: int) -> bool:
s = num - 1
Expand All @@ -25,199 +27,14 @@ def rabinMiller(num: int) -> bool:
return True


def isPrime(num: int) -> bool:
if num < 2:
return False

lowPrimes = [
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,
181,
191,
193,
197,
199,
211,
223,
227,
229,
233,
239,
241,
251,
257,
263,
269,
271,
277,
281,
283,
293,
307,
311,
313,
317,
331,
337,
347,
349,
353,
359,
367,
373,
379,
383,
389,
397,
401,
409,
419,
421,
431,
433,
439,
443,
449,
457,
461,
463,
467,
479,
487,
491,
499,
503,
509,
521,
523,
541,
547,
557,
563,
569,
571,
577,
587,
593,
599,
601,
607,
613,
617,
619,
631,
641,
643,
647,
653,
659,
661,
673,
677,
683,
691,
701,
709,
719,
727,
733,
739,
743,
751,
757,
761,
769,
773,
787,
797,
809,
811,
821,
823,
827,
829,
839,
853,
857,
859,
863,
877,
881,
883,
887,
907,
911,
919,
929,
937,
941,
947,
953,
967,
971,
977,
983,
991,
997,
]

if num in lowPrimes:
return True

for prime in lowPrimes:
if (num % prime) == 0:
return False

return rabinMiller(num)


def generateLargePrime(keysize: int = 1024) -> int:
while True:
num = random.randrange(2 ** (keysize - 1), 2 ** (keysize))
if isPrime(num):
if prime_check(num):
return num


if __name__ == "__main__":
num = generateLargePrime()
print(("Prime number:", num))
print(("isPrime:", isPrime(num)))
print(("isPrime:", prime_check(num)))
57 changes: 11 additions & 46 deletions maths/primelib.py
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Original file line number Diff line number Diff line change
Expand Up @@ -8,7 +8,6 @@

Overview:

isPrime(number)
sieveEr(N)
getPrimeNumbers(N)
primeFactorization(number)
Expand Down Expand Up @@ -38,41 +37,7 @@

"""

from math import sqrt


def isPrime(number):
"""
input: positive integer 'number'
returns true if 'number' is prime otherwise false.
"""

# precondition
assert isinstance(number, int) and (
number >= 0
), "'number' must been an int and positive"

status = True

# 0 and 1 are none primes.
if number <= 1:
status = False

for divisor in range(2, int(round(sqrt(number))) + 1):

# if 'number' divisible by 'divisor' then sets 'status'
# of false and break up the loop.
if number % divisor == 0:
status = False
break

# precondition
assert isinstance(status, bool), "'status' must been from type bool"

return status


# ------------------------------------------
from prime_check import prime_check


def sieveEr(N):
Expand Down Expand Up @@ -129,7 +94,7 @@ def getPrimeNumbers(N):
# if a number is prime then appends to list 'ans'
for number in range(2, N + 1):

if isPrime(number):
if prime_check(number):

ans.append(number)

Expand Down Expand Up @@ -164,11 +129,11 @@ def primeFactorization(number):
ans.append(number)

# if 'number' not prime then builds the prime factorization of 'number'
elif not isPrime(number):
elif not prime_check(number):

while quotient != 1:

if isPrime(factor) and (quotient % factor == 0):
if prime_check(factor) and (quotient % factor == 0):
ans.append(factor)
quotient /= factor
else:
Expand Down Expand Up @@ -317,8 +282,8 @@ def goldbach(number):
isinstance(ans, list)
and (len(ans) == 2)
and (ans[0] + ans[1] == number)
and isPrime(ans[0])
and isPrime(ans[1])
and prime_check(ans[0])
and prime_check(ans[1])
), "'ans' must contains two primes. And sum of elements must been eq 'number'"

return ans
Expand Down Expand Up @@ -462,11 +427,11 @@ def getPrime(n):

# if ans not prime then
# runs to the next prime number.
while not isPrime(ans):
while not prime_check(ans):
ans += 1

# precondition
assert isinstance(ans, int) and isPrime(
assert isinstance(ans, int) and prime_check(
ans
), "'ans' must been a prime number and from type int"

Expand All @@ -486,7 +451,7 @@ def getPrimesBetween(pNumber1, pNumber2):

# precondition
assert (
isPrime(pNumber1) and isPrime(pNumber2) and (pNumber1 < pNumber2)
prime_check(pNumber1) and prime_check(pNumber2) and (pNumber1 < pNumber2)
), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

number = pNumber1 + 1 # jump to the next number
Expand All @@ -495,7 +460,7 @@ def getPrimesBetween(pNumber1, pNumber2):

# if number is not prime then
# fetch the next prime number.
while not isPrime(number):
while not prime_check(number):
number += 1

while number < pNumber2:
Expand All @@ -505,7 +470,7 @@ def getPrimesBetween(pNumber1, pNumber2):
number += 1

# fetch the next prime number.
while not isPrime(number):
while not prime_check(number):
number += 1

# precondition
Expand Down
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