def IsPrimeTruncatable(n, ndigits):
    if (n > 100):
        if (prime.isprime(n) == False):
            for i in range(2, ndigits):
                if (prime.isprime(n // 10**i) == False
                        or prime.isprime(n % 10**i) == False):
                    return False
Exemple #2
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def N(d,n=10):
    """For an n-digit prime, d is the digit that reappears."""
    primes,dict = [], M()
    if dict[d] == n-1:
        to_permute = list(repeat(str(d),n)) #['1','1','1','1']
        digits = [str(k) for k in range(10) if k!=d]
        current_permute = int("".join(to_permute))
        if prime.isprime(current_permute): primes.append(current_permute)
        for i in range(n):
            for digit in digits:
                to_permute[i] = digit
                cur_num = int("".join(to_permute))
                if prime.isprime(cur_num):
                    primes.append(cur_num)
            to_permute[i] = str(d)
        return primes
    if dict[d] == n-2:
        to_permute = list(repeat(str(d),n)) #['1','1','1','1']
        digits = [str(k) for k in range(10) if k!=d]
        double_digits = list(product(digits,digits))
        current_permute = int("".join(to_permute))
        if prime.isprime(current_permute): primes.append(current_permute)
        for i in range(n-1):
            for j in range(1,n):
                for pair in double_digits:
                    to_permute[i] = pair[0]
                    to_permute[j] = pair[1]
                    cur_num = int("".join(to_permute))
#                    print "on",cur_num
                    if prime.isprime(cur_num): 
 #                       print cur_num,"PRIME"
                        primes.append(cur_num)
                to_permute[i] = str(d)
                to_permute[j] = str(d)
        return [k for k in primes if len(str(k))==n]
Exemple #3
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def l_r_primes(n):
    prime_left = prime_right = False
    for i in xrange(1, len(str(n))):
        l = n % pow(10, i)
        r = n / pow(10, i)
        if (not prime.isprime(l)) or (not prime.isprime(r)):
            return False
    return True
Exemple #4
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def test_time_taken_to_calculate():

    t0 = time.time()
    for i in range(2, 100000):
        prime.isprime(i)
    t1 = time.time()
    t = t1 - t0
    assert t < 0.4
Exemple #5
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def answer():
    # observation: cannot be 8 or 9 due to divisibility by 3
    for n in range(7, 0, -1):
        possibilities = map(tuple_to_int, permutations(range(n, 0, -1)))
        for candidate in possibilities:
            if isprime(candidate):
                return candidate
def f():
    for i in reversed(range(1, 547)):
        for j in range(1, 549-i):
            print j, i
            if isprime(sum(islice(sieve, j, i))):
                print j-i+1
                return sum(islice(sieve, j, i))
def bruteforce():
    count=1  # 1/2  is special 
    for d in range(3,N+1):
        if prime.isprime(d):
            count+=d-1
        else:
            count+=count_bruteforce(d)  # error
Exemple #8
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def answer(limit=1000000):
    _refresh(limit // pow(10, sqrt(log10(limit))-1))
    for length in range(int(sqrt(limit)), 0, -1):
        for end in range(len(prime_list), length-1, -1):
            candidate = sum(prime_list[end-length:end])
            if candidate < limit and isprime(candidate):
                return candidate
Exemple #9
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def answer(limit=1000000):
    _refresh(limit // pow(10, sqrt(log10(limit)) - 1))
    for length in range(int(sqrt(limit)), 0, -1):
        for end in range(len(prime_list), length - 1, -1):
            candidate = sum(prime_list[end - length:end])
            if candidate < limit and isprime(candidate):
                return candidate
Exemple #10
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def check_length(n, below):
    maxprime = 0
    for x in xrange(0, below):
        total = sum(prime.prime_list[x:x+n])
        if total > below: break
        if prime.isprime(total): maxprime = total
    return maxprime
Exemple #11
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def gen_pnr(size, m):
    while True:
        # 1 шаг
        p = prime.gen_prime(size)
        assert p % 4 == 1
        assert sympy.isprime(p)

        # 2 шаг (страница 168, алгоритм 7.8.1)
        a, b = get_zi_factors(p, 1)
        assert a * a + b * b == p

        # 3 шаг
        t_set = [2 * a, -2 * a, 2 * b, -2 * b]
        for t in t_set:
            n = p + 1 + t
            rs = [n // 2, n // 4]
            for r in rs:
                if prime.isprime(r):
                    assert sympy.isprime(r)
                    # шаг 4
                    if p != r:
                        for i in range(1, m + 1):
                            if pow(p, i, r) == 1:
                                break
                        else:
                            return p, n, r
Exemple #12
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def answer():
    # observation: cannot be 8 or 9 due to divisibility by 3
    for n in range(7, 0, -1):
        possibilities = map(tuple_to_int, permutations(range(n, 0, -1)))
        for candidate in possibilities:
            if isprime(candidate):
                return candidate
def ProjectEuler37():
    """
    The number 3797 has an interesting property. Being prime itself, 
    it is possible to continuously remove digits from left to right, 
    and remain prime at each stage: 3797, 797, 97, and 7. 
    Similarly we can work from right to left: 3797, 379, 37, and 3.
    Find the sum of the only eleven primes that are both truncatable from left to right and right to left.
    NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
    Solution:  
    1 is not prime, so two digits can only be 37 73 
    then, for number has 3 or more digits, those must be started and ended with 3 or 7
    but the digits between can be combination_with_repeation of [1,3,7,9]
    """
    count = 2
    numbers = [
        37, 73, 23, 53
    ]  # I miss the first two 23, 35,  filter the 2digits combination of [2 3 5 7]
    MaxDigits = 10
    TotalNo = 11
    for d in range(3, MaxDigits + 1):
        # generate a list of possible numbers
        for n in ListOfCandiates(d):
            if (all(prime.isprime(i) for i in ListOfTruncatble(n, d))):
                count = count + 1
                numbers.append(n)
                print(n)
            if (len(numbers) == TotalNo): break
        if (len(numbers) == TotalNo): break
    print(numbers)
    print(sum(numbers))
Exemple #14
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def problem10():
    """
    The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
    Find the sum of all the primes below two million.    
    Answer:   142913828922
    """
    from prime import isprime
    print("problem10:", sum([i for i in range(2, 2000000) if isprime(i)]))
Exemple #15
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def is_left_truncatable(i):
    while True:
        if prime.isprime(i):
            if i > 10:
                i = int("".join(list(str(i))[1::]))
            else:
                return True
        else:
            return False
def countProperFaction(d):
    """ for non-prime number, get the list of factor
    proper factions for denumerator no bigger than 1000: 304191   (tested correctly)
    """
    if prime.isprime(d):
         return (d-1)
    else:
        #return count_bruteforce(d)
        return factorset_union(d)
def problem58():
    numOnDiagonal, width, noOfPrimes = 13, 7, 8 
    while noOfPrimes*10 > numOnDiagonal:
	nextWidth, square = width+2, width*width
	nextSquare = nextWidth*nextWidth
	result = xrange(square+width+1, nextSquare+1, width+1)
	noOfPrimes = noOfPrimes+ len(filter(lambda n: prime.isprime(n), result))
	numOnDiagonal = numOnDiagonal+4
	width = nextWidth
    return width
Exemple #18
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def answer(alim=1000, blim=1000):
    maxn = 0
    for a in range(-alim+1, alim):
        for b in range(-blim+1, blim):
            n = 0
            while isprime(pow(n, 2) + a*n + b):
                n += 1
            if n > maxn:
                maxa, maxb, maxn = a, b, n
    return maxa * maxb
Exemple #19
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def main():
    i = 11
    t = 10
    res = 0
    while i > 0:
        if prime.isprime(t) and l_r_primes(t):
            res += t
            i -= 1
        t += 1
    print res
Exemple #20
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def answer():
    for candidate in count(3, 2):
        if isprime(candidate):
            continue
        for p in prime_list:
            remainder = candidate - p
            root = sqrt(remainder // 2)
            if root == int(root):
                break
        else:
            return candidate
Exemple #21
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def answer():
    for candidate in count(3, 2):
        if isprime(candidate):
            continue
        for p in prime_list:
            remainder = candidate - p
            root = sqrt(remainder//2)
            if root == int(root):
                break
        else:
            return candidate
def phi(n):
    """ if it is prime number, n/phi(n) is small near 1
    but for prime number  phi(n)=n-1, 
    
    """
    if isprime(n):
        return n - 1
    else:
        s = []
        #to-do
        return len(s)
Exemple #23
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def is_right_truncatable(i):
    while True:
        if prime.isprime(i):
            if i > 10:
                a = list(str(i))
                a.pop()
                i = int("".join(a))
            else:
                return True
        else:
            return False
Exemple #24
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def f(n):
    result = []
    number = 0
    for i in count(91):
        if i%2 == 0 or i%5 == 0:
            continue
        if (not isprime(i)) and is_ok(i):
            result.append(i)
            number += 1
            if number == n:
                break
    return sum(result)
Exemple #25
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def pandigital(order):
    nums = [str(i) for i in xrange(1, order+1)]
    product = []
    for num in per(nums):
        num = ''.join(num)
        if isprime(int(num)) and check(num, order):
            product.append(int(num))
        else:
            continue
    if product:
        return max(product)
    else:
        return None
Exemple #26
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def prime_family_length(n, digits):
    if cache.has_key((n, digits)): return cache[n, digits]

    num, nums, count = list(str(n)), [], 0
    if len(dict.fromkeys(num[d] for d in digits).keys()) > 1:
        return cache.setdefault((n, digits), 0)                                # The digits must have the same number

    for d in range(0 in digits and 1 or 0, 10):                                 # Ensure 0 is not the first digit
        for x in digits: num[x] = str(d)
        n = int(''.join(num))
        if prime.isprime(n): count += 1
        nums.append(n)
    for n in nums: cache[n, digits] = count
    return count
Exemple #27
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def e58():

    maxnum = 20000
    prime_count = 0
    count = 1
    for n in xrange(2, maxnum):
        count += 4
        x = (2 * n - 1) ** 2
        for m in range(1, 4):
            if prime.isprime(x - 2 * (n - 1) * m):
                prime_count += 1
        ratio = float(prime_count) / count
        if ratio <= 0.1:
            print 2 * n - 1, prime_count, '/', count, '=', ratio
            break
Exemple #28
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def answer():
    for numbers in combinations_with_replacement(range(10), 4):
        perms_l = [digits_to_num(n) for n in permutations(numbers)]
        perms_s = set(perms_l)
        for fst_index, fst in enumerate(perms_l):
            if fst <= 1487:  # rule out given value
                continue
            for snd_index in range(fst_index + 1, len(perms_l)):
                snd = perms_l[snd_index]
                dif = snd - fst
                if dif == 0:
                    continue
                thrd = snd + dif
                if thrd in perms_s:
                    if all(isprime(n) for n in (fst, snd, thrd)):
                        return fst, snd, thrd
Exemple #29
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def answer():
    for numbers in combinations_with_replacement(range(10), 4):
        perms_l = [digits_to_num(n) for n in permutations(numbers)]
        perms_s = set(perms_l)
        for fst_index, fst in enumerate(perms_l):
            if fst <= 1487: # rule out given value
                continue
            for snd_index in range(fst_index+1, len(perms_l)):
                snd = perms_l[snd_index]
                dif = snd-fst
                if dif == 0:
                    continue
                thrd = snd+dif
                if thrd in perms_s:
                    if all(isprime(n) for n in (fst, snd, thrd)):
                        return fst, snd, thrd
Exemple #30
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#!/usr/bin/python3

import prime

MAX = 10000
prime._refresh(MAX)
squares = dict.fromkeys((x*x for x in range(1, MAX)), 1)

for x in range(35, MAX, 2):
    if not prime.isprime(x):
        is_goldbach = 0
        for p in prime.prime_list:
            if p >= x: break
            key = (x-p)/2
            if key in squares:
                is_goldbach = 1
                break
        if not is_goldbach:
            print(x)
            break

Exemple #31
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from math import sqrt
import prime

primes = filter(lambda k: prime.isprime(k), xrange(2,51))
 
mult = lambda x: reduce(lambda y, z: y * z, x, 1)
 
translate = lambda x: mult(primes[i] ** ((x[i] - 1) // 2) for i in range(len(x)))
 
def generator(limit):
    l = [1] * 14
    while l[13] < limit:
        i = 13
        while i > 0 and (l[i] == l[i-1]):
            l[i] = 1
            i -= 1
        l[i] += 2
        yield l
 
if __name__ == '__main__':
    result = min(translate(l) for l in generator(13) if mult(l) > 4000000)
    print("The result is:", result)
Exemple #32
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def listprimes():
	for i in range(250):
		if (p.isprime(i)):
			print(i)
Exemple #33
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	def test_seven_is_prime(self):
		self.assertTrue(prime.isprime(7))
Exemple #34
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	def test_below2_notprime(self):
		for i in xrange(1, -10, -1):
			self.assertFalse(prime.isprime(i), msg = "Prime numbers must be greater than 1.")
Exemple #35
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	def test_455_not_prime(self):
		self.assertFalse(prime.isprime(452))
Exemple #36
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from prime import is_prime_prob, isprime
import time

base = 2
exponent = 21701
starttime = time.time()
count = 0

try:
    while True:
        cur = time.time()
        print(f"Checking {base}^{exponent}... ", end='')
        if not isprime(exponent):
            exponent += 2
            print()
            continue
        if is_prime_prob(base**exponent - 1):
            print(f"M({exponent}) is probably prime")
            break
        exponent += 2
        count += 1
        end = time.time() - cur
        print(f"{end:.2f} seconds")
except KeyboardInterrupt:
    print("Found {} probable primes in {} seconds".format(
        count,
        time.time() - starttime))
Exemple #37
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get_ipython().run_cell_magic('writefile', 'prime.py', "'''\nIt is  a prime number\n'''\ndef isprime(num):\n    '''\n    It is\n    '''\n    if num in(0, 1):\n        return False\n    for prime in range(2, num-1):\n        if num % prime == 0:\n            return False\n        return True")


# In[4]:


get_ipython().system(' pylint prime.py')


# In[5]:


import prime
prime.isprime(199)


# # USING UNIT TEST

# In[6]:


get_ipython().run_cell_magic('writefile', 'newprime.py', '\nimport unittest\nimport prime\n\nclass primenumber(unittest.TestCase):\n    def testprime(self):\n        Number = 32\n        result = prime.isprime(Number)\n        self.assertEquals(result, False)\n\n        \n    def testprimenum(self):\n        Num = 199\n        res = prime.isprime(Num)\n        self.assertEquals(res, True)\n\n        \n        \nif __name__ == "__main__":\n    unittest.main()')


# In[7]:


get_ipython().system(' python newprime.py')
Exemple #38
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 def is_prime(n):
     return prime.isprime(n)
Exemple #39
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import root
import prime
import key
li = []
print("give the range in which you want prime numbers")
print("start=", end=" ")
lower = int(input())
print("last=", end=" ")
print("should no exceed 1024", end=" ")
upper = int(input())
print("prime between", lower, "and", upper, "are:")
for num in range(lower, upper):
    if (prime.isprime(num)):
        print(num, end=" ")
        li.append(num)
print()
print("select a prime", end=" ")
q = int(input())
if q not in li:
    f1 = 1
    while (f1):
        if q not in li:
            print("please select the prime number from  below list only")
            print(li)
            q = int(input())
            if q in li:
                f1 = 0
print("primitive roots list")
li = []
print("enter lower and upper limits of primitive roots")
print("upper limit should not execeed  " + str(q))
Exemple #40
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def is_8_prime_family(p, d):
    c = 0
    for r in '0123456789':
        np = int(string.replace(p, d, r))
        if(np > 100000 and np < 999999 and prime.isprime(np)): c += 1
    return c==8
#!/usr/bin/env python
# -*- coding: utf-8 -*-
import prime

max_pair = (0, 0, 0)
for a in xrange(-999, 1000):
    for b in xrange(max(2, 1 - a), 1000):  # b >= 2, a + b + 1 >= 2
        n, count = 0, 0
        while True:
            v = n * n + a * n + b
            prime._refresh(v)
            if prime.isprime(v):
                count = count + 1
            else:
                break
            n = n + 1
        if count > max_pair[2]:
            max_pair = (a, b, count)

print max_pair[0] * max_pair[1]
Exemple #42
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def is_truncatable_prime(n):
    n_str = str(n)
    if len(n_str) == 1: return False
    leftwise  = [int(n_str[:i]) for i in range(1, len(n_str))]
    rightwise = [int(n_str[i:]) for i in range(len(n_str))]
    return all(isprime(i) for i in chain(leftwise, rightwise))
Exemple #43
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def test_prime_positive():

    assert prime.isprime(2) == True
    assert prime.isprime(20) == False
    assert prime.isprime(3)
    assert not prime.isprime(4)
Exemple #44
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import prime
print prime.prime(11)
print prime._isprime(32)
print prime.isprime(11)
Exemple #45
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def test_missing_param():

    with pytest.raises(ValueError) as ex_info:
        prime.isprime(-2)
    assert ex_info.type == ValueError
Exemple #46
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	def test_zeronot_prime(self):
		self.assertFalse(prime.isprime(0), msg = "Prime numbers must be greater than 1.")
Exemple #47
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def test_check_range_of_prime():
    with pytest.raises(TypeError):
        prime.isprime(False)
Exemple #48
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	def test_five_is_prime(self):
		self.assertTrue(prime.isprime(5))
Exemple #49
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def test_check_prime_test():
    assert prime.isprime(200) == False
Exemple #50
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It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when n = 41, 41^2 + 41 + 41 is clearly divisible by 41.

Using computers, the incredible formula  n^2 - 79n + 1601 was discovered, which produces 80 primes for the consecutive values n = 0 to 79. The product of the coefficients, -79 and 1601, is -126479.

Considering quadratics of the form:

n^2 + an + b, where |a| <= 1000 and |b| <= 1000

where |n| is the modulus/absolute value of n
e.g. |11| = 11 and |4| = 4
Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n = 0.

'''

import prime

max_pair = (0,0,0)
for a in xrange(-999, 1000):
    for b in xrange(max(2, 1-a), 1000): # b >= 2, a + b + 1 >= 2
        n, count = 0, 0
        while True:
            v = n*n + a*n + b
            prime._refresh(v)
            if prime.isprime(v): count = count + 1
            else: break
            n = n + 1
        if count > max_pair[2]:
            max_pair = (a,b,count)

print max_pair[0] * max_pair[1]
# -*- coding: utf-8 -*-
from __future__ import print_function, unicode_literals, absolute_import, division
"""
We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. 
    For example, 2143 is a 4-digit pandigital and is also prime.
What is the largest n-digit pandigital prime that exists?
"""

digits = "123456789"
from prime import isprime
from itertools import permutations

from tuple_list_to_int_list import tuple_list_to_int_list

for i in range(9, 3, -1):
    l = [
        j for j in tuple_list_to_int_list(permutations(digits[:i]))
        if isprime(j)
    ]
    #print i, l
    if any(l):
        print("largest n-digit pandigital prime ", max(l))
        break