Esempio n. 1
0
def E49():
    prime_perm = [ ]
    for i in range(1487, 10000):
        if is_prime(i) == False: continue

        plist = list(itertools.permutations(str(i)))
        for each_num in plist:
            num =  "".join(map(str, each_num))
            if is_prime(num) == True:
                prime_perm.append(num)

        len_p = len(prime_perm)
        for j in range(0, len_p-1):
            for k in range(j+1, len_p):
                if prime_perm[k] == prime_perm[j]: continue

                diff = int(prime_perm[k]) - int(prime_perm[j])
                next_num = int(prime_perm[k]) + diff

                if (str(next_num) in prime_perm) == True :
                    print prime_perm[j], prime_perm[k], next_num


        del prime_perm[:]

    return 0
Esempio n. 2
0
def CheckRight(num):
    devide = 1
    if (is_prime(num) != True):
        return -1

    for i in range(0, len(str(num)) - 1):
        num = num / 10
        if (is_prime(num) != True):
            return -1

    return 0
Esempio n. 3
0
def is_prime_set(vals):
    subsets = itertools.combinations(vals, 2)
    failed_set = set([])
    for a, b in subsets:
        a = str(a)
        b = str(b)
        str1 = a + b
        str2 = b + a
        if not is_prime(int(str1)) or not is_prime(int(str2)):
            return False
    return True
Esempio n. 4
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def E70():
    res = 0
    min_res = 100
    min_i = 100
    p_set = []
    for i in range (3, MAXNUM, 2):
        if is_prime(i) == True:
            continue

        p_set = factor(i)
        if len(p_set) != 2:
            continue

        if int(p_set[0][1])!=1 or int(p_set[1][1])!=1:
            continue

        # [(421, 1), (571, 1)] <- both are 1
        cnt = i - (int(p_set[0][0])+int(p_set[1][0])-1)
        if is_perm(i, cnt) == False:
            continue

        res = float(i)/float(cnt)
        if min_res >= res:
            min_res = res
            min_i = i
            #print min_res, min_i, cnt, (1, p_set[0][0], p_set[1][0], i)

    print "result", min_res, min_i
    return 0
Esempio n. 5
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def eight_prime_family(prime, rd):
  c=0
  for digit in '0123456789':
    n = int(string.replace(prime, rd, digit))
    if (n>100000 and is_prime(n)):
      c=c+1
  return c==8
Esempio n. 6
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def main():
    best = int(1000000)
    for i in range(11, 1000, 2):

        if i % 5 == 0:
            i += 2

        patterns = deepcopy(patterns5)
        if i > 100:
            patterns = deepcopy(patterns6)

        for j in range(len(patterns)):

            pattern = fill_pattern(patterns[j], i)
            for k in range(3):

                if pattern[0] == -1 and k == 0:
                    continue

                candidate = generate_number(k, pattern)

                #  print(i, j, k, patterns[j], pattern, candidate, is_prime(candidate), get_family_size(k, pattern))
                if is_prime(candidate) and get_family_size(
                        k, pattern) >= 8 and candidate < best:

                    best = candidate
                    break

    print(best)
Esempio n. 7
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def E70():
    res = 0
    min_res = 100
    min_i = 100
    p_set = []
    for i in range(3, MAXNUM, 2):
        if is_prime(i) == True:
            continue

        p_set = factor(i)
        if len(p_set) != 2:
            continue

        if int(p_set[0][1]) != 1 or int(p_set[1][1]) != 1:
            continue

        # [(421, 1), (571, 1)] <- both are 1
        cnt = i - (int(p_set[0][0]) + int(p_set[1][0]) - 1)
        if is_perm(i, cnt) == False:
            continue

        res = float(i) / float(cnt)
        if min_res >= res:
            min_res = res
            min_i = i
            #print min_res, min_i, cnt, (1, p_set[0][0], p_set[1][0], i)

    print "result", min_res, min_i
    return 0
Esempio n. 8
0
def get_family_size(repeated_num, pattern_fam):
    family_size = 0

    for i in range(repeated_num, 10):
        if is_prime(generate_number(i, pattern_fam)):
            family_size += 1

    return int(family_size)
Esempio n. 9
0
def test_make_pairs():
    print(make_pairs([1, 3, 5]))
    print(make_pairs([7, 9]))
    print(make_pairs([75, 23, 18]))

    test = make_pairs([3, 7, 109, 673])
    for elem in iter(test):
        print(elem, is_prime(elem))
Esempio n. 10
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def P(n):
    all_sum = 0
    i = 0
    while i <= n:
        if (is_prime(i)):
            all_sum += i
        i += 1

    return all_sum
Esempio n. 11
0
def P(n):
    all_sum = 0
    i = 0
    while i <= n:
        if (is_prime(i)):
            all_sum += i
        i += 1

    return all_sum
Esempio n. 12
0
def CheckLeft(num):
    devide = 1
    for i in range(0, len(str(num))):
        devide *= 10
        res = num % devide
        if (is_prime(res) != True):
            return -1

    return 0
Esempio n. 13
0
def main(limit):
	num = 1
	vals = []
	while num < limit:
		val = 2*num**2-1
		vals.append(val)
		if not is_prime(val):
			print val, factor(val)
		num += 1
	return vals
Esempio n. 14
0
def Get_P(n):
    i = 2
    prime_th = 0
    while (1):
        if (prime_th == n):
            return (i - 1)
            break

        if (is_prime(i)):
            prime_th += 1

        i += 1
Esempio n. 15
0
def eight_prime_family(prime, rd):

  c=0

  for digit in '0123456789':

    n = int(string.replace(prime, rd, digit))

    if (n>100000 and is_prime(n)):
      c=c+1

  return c==8
Esempio n. 16
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def Get_P(n) :
    i = 2
    prime_th = 0
    while (1):
        if (prime_th == n):
            return (i-1)
            break

        if (is_prime(i)):
            prime_th += 1

        i += 1
def project_euler_27():
    """Finds the product of a and b for that produces the most primes for 
    consecutive values of n, starting with n = 0. For n^2 + an + b where
    |a| < 1000 and |b| < 1000."""
    best = (0, -1001, -1001)

    for a in range(-999, 1000):
        for b in range(-999, 1000):
            n = 0
            while is_prime(abs(n*n + a*n + b)): n += 1
            if n > best[0]: best = (n, a, b)
    print(best[1]*best[2])
Esempio n. 18
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def pFact(num):
  pfactors = []
  while True:
    j = 2
    while j < num+1:
      if num%j==0 and is_prime(j):
        num = num/j
        pfactors.append(j)
        break
      j+=1
    if num==1:
      break
  return pfactors
Esempio n. 19
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def main():
    answers = list()
    for index_a in range(0, len(primes)):
        if primes[index_a] * 5 >= result: break
        if pairs[index_a] is None: pairs[index_a] = make_pairs([index_a])

        for index_b in range(index_a, len(primes)):
            if all([
                    is_prime(n)
                    for n in iter(make_pairs(answers + [primes[index_b]]))
            ]):
                answers.append(primes[index_b])

                for index_c in range(index_b, len(primes)):
                    if all([
                            is_prime(n) for n in iter(
                                make_pairs(answers + [primes[index_c]]))
                    ]):
                        answers.append(primes[index_c])

                        for index_d in range(index_c, len(primes)):
                            if all([
                                    is_prime(n) for n in iter(
                                        make_pairs(answers +
                                                   [primes[index_d]]))
                            ]):
                                answers.append(primes[index_d])

                                for index_e in range(index_d, len(primes)):
                                    if all([
                                            is_prime(n) for n in iter(
                                                make_pairs(answers +
                                                           [primes[index_e]]))
                                    ]):
                                        answers.append(primes[index_e])
                                        return answers

    return "Failed", answers
Esempio n. 20
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def sol_1():
    def formula(i, j, k):
        return k**2 + i * k + j

    max_primes, resI, resJ = 0, 0, 0
    for i in xrange(-1000, 1000):
        for j in xrange(i, 1000):
            k = 0
            while is_prime(formula(i, j, k)):
                k += 1
            if k - 1 > max_primes:
                max_primes = k - 1
                resI, resJ = i, j

    print resI * resJ
def project_euler_26():
    """Calculates the value of d < 1000 for which 1/d contains the longest
    recurring cycle in its decimal fraction part.
    
    Decimal fraction parts only repeat if d is relatively prime to 10,
    so we filter out non-primes from consideration. Next, the number
    of digits is equal to the multiplicative order of 10 mod d."""
    best, index = 0, 0

    for x in [i for i in range(10,1000) if is_prime(i)]:
        y = mult_order_mod(x)
        if y > best:
            index = x
            best = y
    print(index)
Esempio n. 22
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def main ():
  """
  
  """
  
  #
  primes  = [i for i in range(10**3,10**4) if is_prime(i) and '0' not in str(i)]
  #print primes
  
  for p in primes:
    perms = sorted(list(set([int(''.join(perm)) for perm in permutations(str(p)) if is_prime(int(''.join(perm)))])))
    if len(perms) < 3:continue

    diffDiff = [b-a for a,b in pairwise([y-x for x,y in pairwise(perms)])]
    if 0 in diffDiff:

      print p,perms
      print p,diffDiff
      print 

  
  
  
  pass
Esempio n. 23
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def FindPrimeAndTwiceSquare(n):
    max_twice = math.sqrt(n)
    print n, max_twice
    for i in range(1, int(max_twice)):
        if (2 * (i **2)) > n:
            break

        prime = n - (2 * (i ** 2))
        print prime, n
        if (is_prime(prime)) == True:
            print i, "=", prime, "+", "2 x ", i, "^2"
            return True
        #else :
        #    print "not....",i, "=", prime, "+", "2 x ", i, "^2"

    return False
Esempio n. 24
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def FindPrimeAndTwiceSquare(n):
    max_twice = math.sqrt(n)
    print n, max_twice
    for i in range(1, int(max_twice)):
        if (2 * (i**2)) > n:
            break

        prime = n - (2 * (i**2))
        print prime, n
        if (is_prime(prime)) == True:
            print i, "=", prime, "+", "2 x ", i, "^2"
            return True
        #else :
        #    print "not....",i, "=", prime, "+", "2 x ", i, "^2"

    return False
Esempio n. 25
0
def main ():
  """
  
  """

  maxN = 10**6+1
  maxConsecTerms = 0
  maxPrime = 0

  # make a list of primes
  primes = [i for i in range(2,maxN) if is_prime(i)]

  

  for j,p in enumerate(primes):
    print j/780.

    # make a list of the candidate primes
    cand = [c for c in primes[:j]]
  
    # starting at each prime in the candidate list...
    consecTerms=0
    for ind,c in enumerate(cand):
      candSum = 0
      i = ind
      while candSum < p and i < len(cand):
        candSum += cand[i]
        i       += 1
      # aggregate terms until they equal or exceed the target prime
      #print p,c,candSum
      
      consecTerms = i-ind

      if p == candSum:
        if consecTerms > maxConsecTerms:
          maxPrime = p
          maxConsecTerms = consecTerms
          
          #print p,i-ind #,sum(cand[ind:i]),cand[ind:i]
        break
      continue
    print '****',maxPrime,maxConsecTerms
  print 'And the answer is:',maxPrime,'with a total of',maxConsecTerms,'consecutive terms.'
  pass
Esempio n. 26
0
def CirPrime(num):
    buf = str(num)
    len_buf = len(buf)

    devide = 1
    for i in range (0, len_buf-1):
        devide *= 10

    new_num = num
    for i in range(0, len_buf):
        #print new_num
        if (is_prime(new_num)) :
            d1 = new_num / devide
            d2 = new_num % devide
            new_num = d2 * 10 + d1
        else :
            return -1

    return 0
Esempio n. 27
0
def E69():
    res = 0
    max_res = 0
    max_i = 0
    for i in range (2, MAXNUM):
        if i % 2 == 1:
            continue;
        if is_prime(i) == True:
            continue
        cnt = 1
        for j in range (1, i):
            if gcd(i, j) == 1:
                cnt+=1
        if cnt != 0:
            res = float(i)/float(cnt)
            if max_res < res:
                max_res = res
                max_i = i

    print max_res, max_i
    return 0
Esempio n. 28
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def E69():
    res = 0
    max_res = 0
    max_i = 0
    for i in range(2, MAXNUM):
        if i % 2 == 1:
            continue
        if is_prime(i) == True:
            continue
        cnt = 1
        for j in range(1, i):
            if gcd(i, j) == 1:
                cnt += 1
        if cnt != 0:
            res = float(i) / float(cnt)
            if max_res < res:
                max_res = res
                max_i = i

    print max_res, max_i
    return 0
Esempio n. 29
0
            chart[(i, j)] = result
            return result
        else:
            result = sum_of_primes(i - 1, j) - primes[i - 1]
            chart[(i, j)] = result
            return result


(highest, num_of_terms) = (41, 6)
starting_prime_index = 0
for i in xrange(0, 4):  #index of the starting prime
    m = num_of_terms
    for j in xrange(i + m, 550):  #index of the ending prime
        the_sum = sum_of_primes(i, j)
        if the_sum > 1000000: break  #increment here to test
        if is_prime(the_sum):
            highest = the_sum
            num_of_terms = j - i
            starting_prime_index = i

print highest, "is the sum"
print num_of_terms, "terms in the sum"
print "The sum starts at the prime", primes[starting_prime_index]
print time.clock() - t_0, " seconds to complete"

##k=1000000
##while not is_prime(k):
##    k -= 1
##
##print k, "has index", primes.index(k)
##
Esempio n. 30
0
            chart[(i,j)] = result
            return result
        else:
            result = sum_of_primes(i-1,j) - primes[i-1]
            chart[(i,j)] = result
            return result


(highest, num_of_terms) = (41,6)
starting_prime_index = 0
for i in xrange(0,4): #index of the starting prime
    m = num_of_terms
    for j in xrange(i+m,550): #index of the ending prime
        the_sum = sum_of_primes(i,j)
        if the_sum > 1000000: break #increment here to test
        if is_prime(the_sum):
            highest = the_sum
            num_of_terms = j-i
            starting_prime_index = i


print highest, "is the sum"
print num_of_terms, "terms in the sum"
print "The sum starts at the prime", primes[starting_prime_index]
print time.clock() - t_0, " seconds to complete"


##k=1000000
##while not is_prime(k):
##    k -= 1
##
Esempio n. 31
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#27. Come up with a formula n^2 + an + b for |a|,|b|<=1000 which
#generates the most number of consecutive primes starting from n=0.

## Here's the output:
##-59231  is the product of a and b
##70  is the maximum consecutive number of primes
##8.589944  seconds to complete


from Euler import is_prime
import time
import cProfile

t_0 = time.clock()

max_consecutive = 0

for a in xrange(-1000,1001):
    for b in xrange(-1000,1001):
        for n in xrange(80):
            if not is_prime(n**2+a*n+b):
                break
            elif n > max_consecutive:
                max_consecutive = n+1
                if max_consecutive==70:
                    print a*b, " is the product of a and b"


print max_consecutive, " is the maximum consecutive number of primes"
print time.clock()-t_0, " seconds to complete"
Esempio n. 32
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from Euler import is_prime 
import math

def FindPrimeAndTwiceSquare(n):
    max_twice = math.sqrt(n)
    print n, max_twice
    for i in range(1, int(max_twice)):
        if (2 * (i **2)) > n:
            break

        prime = n - (2 * (i ** 2))
        print prime, n
        if (is_prime(prime)) == True:
            print i, "=", prime, "+", "2 x ", i, "^2"
            return True
        #else :
        #    print "not....",i, "=", prime, "+", "2 x ", i, "^2"

    return False

MAX_LIMIT = 1000000
count = 0
for i in range(3, MAX_LIMIT, 2):
    if (is_prime(i) == True):
        continue

    if (FindPrimeAndTwiceSquare(i) == False):
        print "(DONE) result = [",i,"]"
        exit(0)
Esempio n. 33
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#!/usr/bin/python -tt
import sys
sys.path.append('/Users/admin/Desktop/python-work/Project_Euler/primes')

from Euler import prime_sieve, is_prime
 
nmax = 0;
primes = prime_sieve(1000)
for a in range(-999,999,2):
  for b in primes:
    n = 1
    while is_prime(n**2 + a*n + b): n += 1
    if n>nmax: nmax, p = n, a*b
 
print "Answer to PE27 = ",p

def main():
  print 'hello'

# Standard boilerplate to call the main() function.
if __name__ == '__main__':
  main()

Esempio n. 34
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from Euler import prime_sieve, is_prime

max = 1000000
primes = prime_sieve(max)
prime_sum = [0]

sum = 0
count = 0
while (sum<terms and is_prime(n)):
            (terms, max_prime) = (j-i, n)

print "Project Euler 50 Solution = ", max_prime, " with ", terms, " terms"
Esempio n. 35
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def right_prime(n):
  if len(str(n)) ==1:return is_prime(n)
  return is_prime(n) and right_prime(int(str(n)[1:]))
Esempio n. 36
0
from Euler import is_prime

num_diag_primes = 3
step_length = 2
corner = 9

while float(num_diag_primes) / (2 * step_length + 1) > 0.1:
    step_length += 2
    for i in range(0, 3):
        corner += step_length
        if is_prime(corner):
            num_diag_primes += 1
    corner += step_length

print(step_length + 1)

# SOLVED : 26241
Esempio n. 37
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def genPrimes(maxN):
    primes = []
    for n in range(2, maxN + 1):
        if is_prime(n):
            primes.append(n)
    return primes
Esempio n. 38
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def left_prime(n):
  if len(str(n)) ==1:return is_prime(n)
  return is_prime(n) and left_prime(int(str(n)[:-1]))
Esempio n. 39
0
                BUF[a4] = 1
                for a5 in range(1, 8):
                    if (BUF[a5] == 1):
                        continue
                    BUF[a5] = 1
                    for a6 in range(1, 8):
                        if (BUF[a6] == 1):
                            continue
                        BUF[a6] = 1
                        for a7 in range(1, 8):
                            if (BUF[a7] == 1):
                                continue
                            count += 1
                            buf = "%d%d%d%d%d%d%d" % (a1, a2, a3, a4, a5, a6,
                                                      a7)
                            if (is_prime(int(buf)) == True):
                                print "prime = ", buf
                            BUF[a7] = 0
                        BUF[a6] = 0
                    BUF[a5] = 0
                BUF[a4] = 0
            BUF[a3] = 0
        BUF[a2] = 0
'''
for a1 in range(1, 10):
    BUF = [0,0,0,0,0,0,0,0,0,0]
    BUF[a1] = 1
    for a2 in range(1, 10):
        if (BUF[a2] == 1):
            continue
        BUF[a2] = 1
Esempio n. 40
0
#!/usr/bin/python

from Euler import is_prime
from time import clock

# start a process timer
clock()

# setup a counter
max = 0

# get a list of primes
z = [n for n in range(10**6+1) if is_prime(n)]
lenght = len(z)

for a in range(0, lenght-1):
  #
  t = 0
  sum = 0
  wyrazy = 0

  #
  for i in range(a, lenght-1):
    sum = sum + z[i]
    if sum > 10**6:
      break
    wyrazy += 1
    if is_prime(sum) and sum != z[i] and wyrazy > max:
      r = sum
      max = wyrazy
print(r)
Esempio n. 41
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#!/usr/bin/python

from Euler import is_prime
from sys import stdout

print "{ ",

for n in range(2,10**6):
	if is_prime(n) :
		stdout.write("'%s': 1, " % (str(n)))

print "}"

Esempio n. 42
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def test(n):
    for factor in divisors(n):
        if not is_prime(factor + (n / factor)):
            return False
    return True
'''
What is the side length of the square spiral for which the ratio of primes
along both diagonals first falls below 10%?
'''

from Euler import is_prime, itertools

# consider a layer N
# for example, N = 3
# .......         .......
# .NNNNN.    S    .C...C.
# .N...N.    S    ..XXXX.
# .N...N. => S => ..XXXX.
# .N...N.    S    ..XXXX.
# .NNNNN.    S    .C.....
# .......         .......

count = 0
for N in itertools.count(start=2):
    S = 2*N-1
    X = (S-1)*(S-2)
    i = X+1
    count += sum(is_prime(i+j*(S-1)) for j in range(3))
    total = 4*N-3
    if count/total < 0.1:
        break

ans = S
print(ans)
def project_euler_3():
    '''Prints the largest prime factor of 600851475143.
    See the is_prime method in Euler.py for more details.'''
    print(max(i for i in range(1, int(600851475143**.5) +1) if 600851475143 % i == 0 and is_prime(i)))
Esempio n. 45
0
<i>n</i>&sup2; + <i>an</i> + <i>b</i>, where |<i>a</i>| &lt; 1000 and |<i>b</i>| &lt; 1000<br /><br />
<div class="info" style="text-align:left;">where |<i>n</i>| is the modulus/absolute value of <i>n</i><br />e.g. |11| = 11 and |&minus;4| = 4</div>
</blockquote>
<p>Find the product of the coefficients, <i>a</i> and <i>b</i>, for the quadratic expression that produces the maximum number of primes for consecutive values of <i>n</i>, starting with <i>n</i> = 0.</p>
</div><br />
<br /></div>
"""

from Euler import is_prime

max_cnt = 0
max_a = 0
max_b = 0

for a in range(-1000, 1001):
    for b in range(-1000, 1001):
        n = 0
        while (True):
            result = (n * n) + (a * n) + b
            if (is_prime(result)):
                n += 1
            else:
                if (max_cnt < n):
                    max_cnt = n
                    max_a = a
                    max_b = b
                break

print max_cnt, max_a, max_b
print "result=", (max_a * max_b)
Esempio n. 46
0
#!/usr/bin/python -Wall
# -*- coding: utf-8 -*-
"""
<div id="content">
<div style="text-align:center;" class="print"><img src="images/print_page_logo.png" alt="projecteuler.net" style="border:none;" /></div>
<h2>Largest prime factor</h2><div id="problem_info" class="info"><h3>Problem 3</h3><span>Published on Friday, 2nd November 2001, 06:00 pm; Solved by 281868; Difficulty rating: 5%</span></div>
<div class="problem_content" role="problem">
<p>The prime factors of 13195 are 5, 7, 13 and 29.</p>
<p>What is the largest prime factor of the number 600851475143 ?</p>
<!--
Note: This problem has been changed recently, please check that you are using the right number.
-->
</div><br />
<br /></div>
"""

from Euler import is_prime

#limit = 13195
limit = 600851475143

i = 3
max_num = 0
for i in range(i, 10000):
    if (is_prime(i)):
        if (limit % i == 0):
            temp = limit // i
            max_num = i

print "max =", max_num
Esempio n. 47
0
import math


def FindPrimeAndTwiceSquare(n):
    max_twice = math.sqrt(n)
    print n, max_twice
    for i in range(1, int(max_twice)):
        if (2 * (i**2)) > n:
            break

        prime = n - (2 * (i**2))
        print prime, n
        if (is_prime(prime)) == True:
            print i, "=", prime, "+", "2 x ", i, "^2"
            return True
        #else :
        #    print "not....",i, "=", prime, "+", "2 x ", i, "^2"

    return False


MAX_LIMIT = 1000000
count = 0
for i in range(3, MAX_LIMIT, 2):
    if (is_prime(i) == True):
        continue

    if (FindPrimeAndTwiceSquare(i) == False):
        print "(DONE) result = [", i, "]"
        exit(0)
Esempio n. 48
0
                    continue
                BUF[a4] = 1
                for a5 in range(1, 8):
                    if (BUF[a5] == 1):
                        continue
                    BUF[a5] = 1
                    for a6 in range(1, 8):
                        if (BUF[a6] == 1):
                            continue
                        BUF[a6] = 1
                        for a7 in range(1, 8):
                            if (BUF[a7] == 1):
                                continue
                            count += 1
                            buf = "%d%d%d%d%d%d%d" % (a1,a2,a3,a4,a5,a6,a7)
                            if (is_prime(int(buf)) == True):
                                print "prime = ", buf
                            BUF[a7] = 0
                        BUF[a6] = 0
                    BUF[a5] = 0
                BUF[a4] = 0
            BUF[a3] = 0
        BUF[a2] = 0


'''
for a1 in range(1, 10):
    BUF = [0,0,0,0,0,0,0,0,0,0]
    BUF[a1] = 1
    for a2 in range(1, 10):
        if (BUF[a2] == 1):
Esempio n. 49
0
def r_p(p):
    for i in trunc_r(p):
        if not is_prime(i):
            return False
    return True
Esempio n. 50
0
from Euler import prime_sieve, is_prime

max = 1000000
primes = prime_sieve(max)
prime_sum = [0]

sum = 0
count = 0
while (sum < terms and is_prime(n)):
    (terms, max_prime) = (j - i, n)

print "Project Euler 50 Solution = ", max_prime, " with ", terms, " terms"
Esempio n. 51
0
def is_valid(my_list):
    return all((is_prime(str(p[0]) + str(p[1]))) for p in perms(my_list, 2))
Esempio n. 52
0
"""fact = lambda n: reduce (lambda x,y:x*y, range(1,n+1))
 
def mod10(n):
	r = 0

for i in range(1,n+1):
	f = fact(i)
	r = (r + pow(i,f,10)) % 10
	return r
 
 
while True:
	a = raw_input()
	if a == '#':break
	print mod10(int(a))"""
from Euler import is_prime
if is_prime(23):
    print 'hi'
else:
    print 'no'
Esempio n. 53
0
def genPrimes(maxN):
	primes = []
	for n in range(2, maxN+1):
		if is_prime(n):
			primes.append(n)
	return primes
Esempio n. 54
0
"""
<div id="content">
<div style="text-align:center;" class="print"><img src="images/print_page_logo.png" alt="projecteuler.net" style="border:none;" /></div>
<h2>Largest prime factor</h2><div id="problem_info" class="info"><h3>Problem 3</h3><span>Published on Friday, 2nd November 2001, 06:00 pm; Solved by 281868; Difficulty rating: 5%</span></div>
<div class="problem_content" role="problem">
<p>The prime factors of 13195 are 5, 7, 13 and 29.</p>
<p>What is the largest prime factor of the number 600851475143 ?</p>
<!--
Note: This problem has been changed recently, please check that you are using the right number.
-->
</div><br />
<br /></div>
"""


from Euler import is_prime

#limit = 13195
limit = 600851475143

i = 3
max_num = 0
for i in range (i, 10000):
    if (is_prime(i)):
        if (limit % i == 0):
            temp = limit // i
            max_num = i


print "max =", max_num
Esempio n. 55
0
<div class="info" style="text-align:left;">where |<i>n</i>| is the modulus/absolute value of <i>n</i><br />e.g. |11| = 11 and |&minus;4| = 4</div>
</blockquote>
<p>Find the product of the coefficients, <i>a</i> and <i>b</i>, for the quadratic expression that produces the maximum number of primes for consecutive values of <i>n</i>, starting with <i>n</i> = 0.</p>
</div><br />
<br /></div>
"""

from Euler import is_prime

max_cnt = 0
max_a = 0
max_b = 0

for a in range (-1000, 1001):
    for b in range (-1000, 1001):
        n = 0
        while (True):
            result = (n*n) + (a*n) + b
            if (is_prime(result)):
                n += 1
            else:
                if (max_cnt < n):
                    max_cnt = n
                    max_a = a
                    max_b = b
                break


print max_cnt, max_a, max_b
print "result=", (max_a * max_b)