def primes_between(n, m):
primes_list = []
if n > m:
raise ValueError(
'The first input number must be greater than the second')
for i in range(n, m): # Generate all numbers between (n + 1) and (m - 1)
if i >= (m - 1): # The range (i) has reached m - 1
if not is_prime.is_prime(
m - 1
): # If (i OR m-1 - they're the same) is not prime, return the list and function is finished
return primes_list
if is_prime.is_prime(
m - 1
) == True: # If m-1 is prime, add it to the list and return that
primes_list.append(m - 1)
return (primes_list)
if is_prime.is_prime(
i
) == False: # If the integer is not prime, continute to the next one
continue
if is_prime.is_prime(
i
) == True: # If the integer is prime, add it to the list and continue
primes_list.append(
i) # We keep doing this until the value of m-1 is reached
continue
def goldbach(n):
result = []
for num in range(2, n):
temp_list = [(n - num, num)]
if is_prime(num) and is_prime(n - num) and not is_in_list(result, temp_list):
result.append((num, n - num))
return result
def test_is_prime():
'''Make sure we are only getting primes'''
assert is_prime(2) == True
assert is_prime(3) == True
assert is_prime(4) == False
assert is_prime(23) == True
assert is_prime(102) == False
def goldbach(n):
divisor = 1
tuples = []
while divisor <= n / 2:
if is_prime(divisor) and is_prime(n - divisor):
tuples.append((divisor, n - divisor))
divisor += 1
return tuples
def goldbach(n):
result = []
for num in range(2, n):
temp_list = [(n - num, num)]
if is_prime(num) and is_prime(n - num) and not is_in_list(
result, temp_list):
result.append((num, n - num))
return result
def goldbach(n):
divisor = 1
tuples = []
while divisor <= n/2:
if is_prime(divisor) and is_prime(n-divisor):
tuples.append((divisor, n - divisor))
divisor += 1
return tuples
def goldbach(n):
numbers = [(x, y) for x in range(1, n)
for y in range(1, n)
if is_prime(x) # True
if is_prime(y) # True
if x <= y
if (x + y) == n]
return numbers
def goldbach(even_integer):
first_addend, second_addend = even_integer // 2
result = []
while second_addend <= even_integer:
if is_prime(first_addend) and is_prime(second_addend):
result.append((first_addend, second_addend))
first_addend += 1
second_addend -= 1
return result
def test_is_prime(self):
with self.subTest():
self.assertEqual(is_prime(1), False)
with self.subTest():
self.assertEqual(is_prime(2), True)
with self.subTest():
self.assertEqual(is_prime(3), True)
with self.subTest():
self.assertEqual(is_prime(0), False)
with self.subTest():
self.assertEqual(is_prime(-1), False)
def test_float_input(self):
self.assertEqual(is_prime(1.0), False)
self.assertEqual(is_prime(4.0), False)
self.assertEqual(is_prime(4.5), False)
#for num <= 1 return false
#for num <= 3 return true
#for num > 3 check if modulo == 0
#for any other input type - TypeError
#check what happens when FLOATS are used!!!! - only natural numbers can be checked for beeing a prime
def is_quadratic_residue(a, m):
if is_prime(m):
flag = legendre.is_quadratic_residue_legendre(a, m)
return flag
if not is_prime(m):
flag = Jacob.is_quadratic_residue_Jacob(a, m)
return flag
# is_quadratic_residue(11,2011)
# is_quadratic_residue(201111,2011)
# is_quadratic_residue(11,2011*2017)
# is_quadratic_residue(15211,2011*2017)
def test_is_prime():
message = "{} is{} a prime number. Your function returned {}."
true_tests = (14081, 17909, 11117, 9319, 6781, 6329, 719, 6211, 2473, 1877,
11923, 1823, 1409, 1187, 83, 17761, 7561, 4051, 5437, 10949,
2)
for n in true_tests:
assert is_prime(n), message.format(n, "", False)
false_tests = (13035, 15547, 8073, 13559, 5921, 12321, 14541, 12543, 14433,
16123, 4005, 12939, 17145, 2109, 17415, 13673, 14529, 10917,
9571, 5919, 4)
for n in false_tests:
assert not is_prime(n), message.format(n, " not", True)
def prime_divisors(n):
max_prime = 2
if is_prime(n):
return n
else:
t = int(math.sqrt(n))
for k in range(the_nth_prime(1000), the_nth_prime(10000),
2): #the 1000th prime number is not a divisor of n,
# the_nth_prime(10000) is some upper bound I've chosen and improves performances significantly but I wonder
# if there is some closed formula for a lower and upper bound for this problem
#for k in range(1051, t // 2, 2): # I've chosen to start from 1051 which is prime and is not a divisor of 600851475143
if is_prime(k):
if n / k == int(n / k) and k > max_prime:
max_prime = k
return max_prime
def get_next_prime(start_int):
n = start_int
while is_prime(n) == False:
n += 1
return n
def prime_factorisation(n):
if n == 1:
return 1
primes = []
result = []
for i in range(2, n + 1):
if is_prime(i):
primes.append(i)
for p in primes:
counter = 0
if p * p > n:
break
while n % p == 0:
counter += 1
prime_factor = (p, counter)
n //= p
result.append(prime_factor)
if n > 1:
result.append(n)
return result
def prime_number_of_divisors(n):
counter = 0
for i in range(1, n + 1):
if n % i == 0:
counter += 1
return is_prime(counter)
def goldbach(n):
prime_numbers = []
rev_prime_numbers = []
list_of_result = []
result = []
for i in range(2, n):
if is_prime(i):
prime_numbers.append(i)
i = len(prime_numbers)
while i > 0:
i -= 1
rev_prime_numbers.append(prime_numbers[i])
for num in prime_numbers:
for nums in rev_prime_numbers:
if num + nums == n:
list_of_result.append((num, nums))
if len(list_of_result) == 1:
return list_of_result
elif len(list_of_result) == 2:
if max(list_of_result[0]) != max(list_of_result[1]):
return list_of_result
else:
list_of_result.remove(list_of_result[1])
return list_of_result
else:
if len(list_of_result) % 2 == 0:
for num in range(0, len(list_of_result) / 2):
result.append(list_of_result[num])
return result
else:
for num in range(0, len(list_of_result) / 2 + 1):
result.append(list_of_result[num])
return result
def prime_factorize(num: int) -> dict:
"""Returns a prime-factorization tree of a given integer.
@param num: the number to factorize
@type num: int
@return: a prime factorization tree
@rtype: dictj
"""
factorization_tree = Tree({num: {}}, allowed_nodes=2)
factor_queue = [factorization_tree._root_node]
# Continuously factorize the numbers until there are none left.
while len(factor_queue) > 0:
node = factor_queue.pop(0)
number = node.value
# Only non-primes can be further subdivided
if is_prime.is_prime(number) is True:
continue
try:
factor_a, factor_b = next(iter(pairs.pairs(number, primes=False)))
except StopIteration:
break
node_a = factorization_tree.insert(node, factor_a)
node_b = factorization_tree.insert(node, factor_b)
factor_queue.append(node_a)
factor_queue.append(node_b)
return factorization_tree
def generate_primes(start=2, end=0):
while True:
if end and start > end:
break
if ip.is_prime(start):
yield start
start += 1
def zad26(a, b):
if a > 0 and b > 0:
num = 1
a -= 1
for n in num_gen(num, a, b):
if not is_prime(n):
yield n
def obtain_prime_factorisation(N):
"""
Return the prime factorisation of a number.
Inputs:
- N: integer
Outputs:
- a list of prime factors
- a list of the exponents of the prime factors
"""
factors = []
potential_factor = 1
while N > 1:
potential_factor += 1
if is_prime.is_prime(potential_factor):
N, exponent = repeat_divide.repeat_divide_number(
N, potential_factor)
if exponent > 0:
factors.append((potential_factor, exponent))
return factors
def prime_number_of_divisors(n):
if n == 1:
return True
elif n < 1:
return False
number_of_divisors = len(find_divisors(n))
return is_prime(number_of_divisors)
def prime_number_of_divisors(n):
counter = 0
for i in range(1, n + 1):
if n % i == 0:
counter += 1
return is_prime(counter)
def test_not_prime(self):
self.assertEqual(is_prime(4), False, "4 is not prime")
self.assertEqual(is_prime(6), False, "6 is not prime")
self.assertEqual(is_prime(8), False, "8 is not prime")
self.assertEqual(is_prime(9), False, "9 is not prime")
self.assertEqual(is_prime(45), False, "45 is not prime")
self.assertEqual(is_prime(-5), False, "-5 is not prime")
self.assertEqual(is_prime(-8), False, "-8 is not prime")
self.assertEqual(is_prime(-41), False, "-41 is not prime")
def largest_prime_factor(n):
i = 2
while i != n:
if is_prime(i) and n%i == 0:
n = int(n/i)
else:
i += 1
return(i)
def prime_number_of_divisors(number):
num = number
numbers = []
while num >= 1:
if number % num == 0:
numbers.append(num)
num = num - 1
return is_prime(len(numbers))
def list_primes(n):
'''Lists N number of prime numbers'''
i, count = 2, 1
while count <= n:
if primes.is_prime(i):
print(count, ':', i)
count += 1
i += 1
def previous_prime(n):
for i in range(n-1, 2, -1): #Descending list from n-1 to 1 in increments of -1.
if is_prime.is_prime(i) == False: # If not prime, continue the search
continue
else: # If this condition is reached, none of the numbers below are prime
return i
def sum_of_primes(n):
'''Return the sum of all primes less than or equal to n'''
ret = 0
for i in range(2, n + 1):
if is_prime(i):
ret += i
return ret
def prime_factors(n):
primes = []
while n != 1:
for i in range(2, n+1):
if is_prime(i) and n%i == 0:
primes.append(i)
n = n//i
return primes
def phi(n):
if is_prime(n):
# if the number is prime, phi(n) is simply n-1
return n - 1
# else you have to factor it, calculate phi for each factor and multiply them
n_factors = prime_factorization(n)
phi_factors = map(lambda factor: phi_helper(factor[0], factor[1]),
n_factors)
return reduce(lambda x, y: x * y, phi_factors)
def next_prime(n):
#Generate every number bigger than n
for i in range(n + 1, n**100):
if is_prime.is_prime(i) == False:
continue
else:
return i
def goldbach(n):
result = []
prime_addend = 2
while prime_addend <= n / 2:
if is_prime(n - prime_addend):
result.append((prime_addend, n - prime_addend))
prime_addend = next_prime(prime_addend)
return result
def main():
for number in range(100000000):
if is_prime.is_prime(number):
save_data(number)
print("Job took: %s" % (datetime.datetime.now() - start))
input()
def prime_number_of_divisors(n): numDivisors = 0 for iterate in range(1,n+1): if n % iterate == 0: numDivisors+=1 if is_prime.is_prime(numDivisors): return True else: return False
def goldbach(n):
result = []
prime_addend = 2
while prime_addend <= n/2:
if is_prime(n - prime_addend):
result.append((prime_addend, n - prime_addend))
prime_addend = next_prime(prime_addend)
return result
def get_public_exponent(m):
n = m-1
while n > 0:
if gcd(n, m) == 1 and is_prime(n):
return n
n -= 1
return -1
def find_primes_up_to(n):
if n < 2:
return []
primes = [2]
currentNumber = 2
while currentNumber <= n:
if is_prime(currentNumber):
primes.append(currentNumber)
currentNumber = currentNumber + 1
return primes
def prime_number_of_divisors(n):
i = 1
s = 0
while i <= n:
if n % i == 0:
s += 1
i += 1
if is_prime(s):
return True
else:
return False
def prime_number_of_divisors(n):
count_divisors = 0
divisor = 1
while divisor <= n:
if n % divisor == 0:
count_divisors += 1
divisor += 1
if ip.is_prime(count_divisors):
return True
else:
return False
def get_prime_factors(n):
"""Tests all divisors of n that are lower or equal than n/2 and if they are prime, returns them"""
factors = [] # Store prime factors
# Start testing from 2 up to half of the target number,
# the maximum possible prime factor
for i in range(2, n // 2 + 1):
if n % i == 0 and is_prime.is_prime(
i): # If number is a divisor and is prime, return it
factors.append(i)
return factors
def nth_prime(n):
'''Return the nth prime number'''
primes_found = 0
i = 2
while primes_found < n:
if is_prime(i):
primes_found += 1
i += 1
# We return i - 1 here because 1 is added to i at the end of each loop
return i - 1
def test_default():
assert is_prime(11) == True
assert is_prime(5) == True
assert is_prime(30) == False
assert is_prime(17) == True
assert is_prime(6) == False
assert is_prime(10) == False
def test(self):
self.assertEqual(is_prime(0), False, "0 is not prime")
self.assertEqual(is_prime(1), False, "1 is not prime")
self.assertEqual(is_prime(2), True, "2 is prime")
self.assertEqual(is_prime(73), True, "73 is prime")
self.assertEqual(is_prime(75), False, "75 is not prime")
self.assertEqual(is_prime(-1), False, "-1 is not prime")
def prime_factorization(n):
divisor = 2
tuples = []
while n > 1:
if n % divisor == 0 and is_prime(divisor):
power = 0
while n % divisor == 0:
n //= divisor
power += 1
tuples.append((divisor, power))
else:
divisor += 1
return tuples
def euler7(n):
if n == 1:
return 2
num = 1
i = 1
while i < n:
num += 2
if is_prime(num):
i += 1
return num
def goldbach(n):
if n == 0:
raise ZeroDivisionError
result = []
limit = n
for i in range(2, (limit // 2) + 1):
if is_prime(i) is True:
first = i
n -= first
for j in range(n, 0, -1):
if is_prime(j) and n - j == 0:
result.append((first, j))
break
n = limit
if len(result) == 0:
return False
return result
def prime_factorization(n):
dividers = []
counter = 2
p = n
while n != 1:
if is_prime(counter) and n % counter == 0:
dividers.append(counter)
n /= counter
else:
counter += 1
result = []
for i in range(2, p + 1):
if dividers.count(i) > 0:
result.append((i, dividers.count(i)))
return result
def prime_factorization(n):
primes = []
i = 2
while i <= n:
if is_prime(i):
primes.append(i)
i += 1
result = []
for numb in primes:
while n % numb == 0:
result.append(numb)
n /= numb
return result
def goldbach(n): if n <= 2: return False primes = [] result = [] for i in range(1, n): if is_prime(i): primes.append(i) for prime in primes: for another_prime in primes: if prime + another_prime == n and prime <= another_prime: result.append((prime, another_prime)) return result
def prime_factorization(n): arr = [] pow = 0 numb = 2 while n != 1: if is_prime(numb): if n % numb == 0: while n % numb == 0: pow = pow + 1 n = n//numb arr = arr + [(numb, pow)] numb = numb + 1 pow = 0 else: numb =numb + 1 else: numb = numb + 1 return arr
def prime_factorization(n):
if is_prime(n):
return [(n, 1)]
result = []
for i in range(2, n):
times_divided = 0
print("Starting ..")
print(n)
if n % i == 0:
times_divided += 1
n //= i
if times_divided > 0:
print("Appending .. ")
result.append((i, times_divided))
return result
def consecutive_primes(a, b):
"""
Return the number of consecutive primes produced by n^2 + an + b
Args:
a (int): The 'a' coefficient.
b (int): The 'b' coefficient.
Returns:
The number of consecutive primes; zero if the first number is not prime
"""
count = 0
n = 0
while is_prime(n**2 + a*n + b):
count += 1
n += 1
return count
def prime_factors(n, array=None, div=1):
#if first pass, set array to a new instance
if array is None:
array = []
#if n is negative, make it positive
if n < 0:
n = n * -1
#make div a positive int
if div < 1:
div = 1
inc = 1
#if div is > 2 we can increment by 2's, because no primes are even other than 2
if div > 2:
inc = 2
# if we're at the end point. divisors won't be larger than the square root of input
if div > n:
# if array length is still one, then it's a prime number
if len(array) == 0:
array.append(n)
return array
# n is not a multiple of div, so proceed
elif n % div != 0:
return prime_factors(n, array, div+inc)
# if n is a multiple of div, add it
else:
n = n / div
if div not in array and is_prime(div):
array.append(div)
return prime_factors(n, array, div+inc)
# -*- coding: utf-8 -*-
"""
Created on Tue Sep 22 13:33:07 2015
@author: A.KRUG
"""
from is_prime import is_prime
somme = 0
for i in range(1, 1000):
if is_prime(i):
somme = somme + i
print(somme)
#PROJECT EULER PROBLEM 46
from is_prime import is_prime
answer = 0
for each in range(1,1000000,2):
if is_prime(each):
pass
else:
trigger = False
for number in range(each):
diff = each - 2*number**2
if diff < 0:
trigger = True
answer = each
break
if is_prime(diff):
break
if trigger == True:
print(answer)
break
def testCase1(self):
self.assertTrue(is_prime(7), "7 should noot be prime")