# This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://san-ss.is-a-geek.com.ar ######################################################################## from itertools import permutations, combinations, chain from CommonFunctions import find_primes_less_than primes = find_primes_less_than(32000) def is_prime(n): if n == 1: return False limit = int(n ** 0.5) for p in primes: if p > limit: return True if n % p == 0: return False return True len_key = {} len_dig_key = {}
def determine_prime(n):
if n in primes:
return True
if n in non_primes:
return False
if is_prime(n):
primes.add(n)
return True
else:
non_primes.add(n)
return False
if __name__ == '__main__':
list_of_sets = []
maxim = 0
for prime in find_primes_less_than(10000)[1:]:
for i in range(len(list_of_sets)):
s = list_of_sets[i]
enter = True
str_prime = str(prime)
for n in s:
str_n = str(n)
if not determine_prime(int(str_n + str_prime)) or not determine_prime(int(str_prime + str_n)):
enter = False
break
if enter:
newset = s.copy()
newset.add(prime)
if len(newset) == 5:
print("The result is:", sum(newset))
exit(0)
# # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://san-ss.wikidot.com ######################################################################## from CommonFunctions import find_primes_less_than from itertools import islice, count primes = set(find_primes_less_than(1000000)) def is_truncable(i): if i < 10: return False tmp = str(i) for x in range(len(tmp)): if (int(tmp[x:]) not in primes) or (int(tmp[:x + 1]) not in primes): return False return True if __name__ == '__main__': result = sum(islice(filter(is_truncable, primes), 11)) print("The result is:", result)
if n in primes:
return True
if n in non_primes:
return False
if is_prime(n):
primes.add(n)
return True
else:
non_primes.add(n)
return False
if __name__ == '__main__':
list_of_sets = []
maxim = 0
for prime in find_primes_less_than(10000)[1:]:
for i in range(len(list_of_sets)):
s = list_of_sets[i]
enter = True
str_prime = str(prime)
for n in s:
str_n = str(n)
if not determine_prime(
int(str_n + str_prime)) or not determine_prime(
int(str_prime + str_n)):
enter = False
break
if enter:
newset = s.copy()
newset.add(prime)
if len(newset) == 5:
# This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://wiki.san-ss.com.ar ######################################################################## from functools import reduce from CommonFunctions import find_primes_less_than primes = find_primes_less_than(50) 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
for mask in permutations(zeros + ones):
masks.add(mask)
return masks
def apply_mask(n, mask):
str_n = str(n)
result = ""
remain = ""
for i in range(len(mask)):
result += mask[i] and str_n[i] or ""
remain += (not mask[i]) and str_n[i] or ""
return result, int(remain)
if __name__ == '__main__':
primes = find_primes_less_than(1000000)
length = 0
result = None
for prime in takewhile(lambda x: result is None, primes):
if len(str(prime)) > length:
length = len(str(prime))
masks = build_masks(length)
groups = {}
for mask in masks:
res, remain = apply_mask(prime, mask)
if min(res) == max(res):
if mask not in groups:
groups[mask] = {}
if remain not in groups[mask]:
groups[mask][remain] = []
groups[mask][remain].append(prime)
'x' : set()
}
def sam_clock(n):
global numbers
result = 0
while n >= 10:
result += sum(len(numbers[c]) for c in str(n)) * 2
n = sum(int(c) for c in str(n))
result += sum(len(numbers[c]) for c in str(n)) * 2
return result
def max_clock(n):
global numbers
result = 0
prev_n = 'x' * len(str(n))
while n >= 10:
str_n = 'x' * (len(prev_n) - len(str(n))) + str(n)
result += sum(len((numbers[a] | numbers[b]) - (numbers[a] & numbers[b])) for a,b in zip(prev_n, str_n))
prev_n = str(n)
n = sum(int(c) for c in str(n))
str_n = 'x' * (len(prev_n) - len(str(n))) + str(n)
result += sum(len((numbers[a] | numbers[b]) - (numbers[a] & numbers[b])) for a,b in zip(prev_n, str_n))
result += sum(len(numbers[a]) for a in str(n))
return result
if __name__ == '__main__':
primes = (x for x in find_primes_less_than(2 * (10 ** 7)) if x > 10 ** 7)
result = sum(sam_clock(x) - max_clock(x) for x in primes)
print("The result is: {0}", result)
# This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://wiki.san-ss.com.ar # Visit my blog at http://blog.san-ss.com.ar ######################################################################## from CommonFunctions import find_primes_less_than LIMIT = 100000 if __name__ == '__main__': primes = find_primes_less_than(LIMIT) rads = [[1, i] for i in range(LIMIT+1)] for p in primes: for i in range(p, LIMIT+1, p): rads[i][0] *= p print("The result is:", sorted(rads)[10000][1])
from CommonFunctions import find_primes_less_than
from itertools import combinations
LIMIT = 120000
primes = find_primes_less_than(LIMIT)
p_to_n = {}
factors = [[set(), 1] for i in range(LIMIT)]
for p in primes:
p_to_n[p] = set()
for i in range(p, LIMIT, p):
p_to_n[p].add(i)
factors[i][0].add(p)
factors[i][1] *= p
result = 0
for b in range(2, LIMIT - 1):
possibles_a = set(range(1, min(LIMIT - b, b)))
possibles_a.difference_update(*(p_to_n[p] for p in factors[b][0]))
for a in possibles_a:
c = a + b
if factors[a][1] * factors[b][1] * factors[c][1] < c:
result += c
print("Result:", result)
#~
#~ result = 0
#~ for c in range(3, LIMIT):
#~ for a, b in ((a, c - a) for a in range(1, c // 2 + 1)):
#~ if (factors[a][0] & factors[b][0]):
#~ continue
# This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://san-ss.is-a-geek.com.ar ######################################################################## from itertools import product, combinations, zip_longest from CommonFunctions import find_primes_less_than primes = find_primes_less_than(350000) def is_prime(n): for p in primes: if p >= n: return True if n % p == 0: return False return True def generator(n, d, rep): def filt_func(t): if t[0][0] == 0 and t[1][0] == 0: return False
# This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://wiki.san-ss.com.ar ######################################################################## from functools import reduce from CommonFunctions import find_primes_less_than primes = find_primes_less_than(50) 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
# but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://wiki.san-ss.com.ar # Visit my blog at http://blog.san-ss.com.ar ######################################################################## from CommonFunctions import find_primes_less_than from itertools import takewhile primes = find_primes_less_than(6 * (10**6)) primes_set = set(primes) def primes_in_range(from_, to_): p_limit = (to_ + 1)**(0.5) prime_set = set(range(from_, to_ + 1)) for p in takewhile(lambda x: x <= p_limit, primes): mod = from_ % p start_n = from_ + (0 if mod == 0 else p - mod) for i in range(start_n, to_ + 1, p): prime_set.discard(i) return prime_set
# This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://san-ss.is-a-geek.com.ar ######################################################################## from CommonFunctions import find_primes_less_than from itertools import count, takewhile primes = find_primes_less_than(int(1000000 ** 0.5)) def is_prime(n): limit = n ** 0.5 for p in primes: if p > limit: return True if n % p == 0: return False return True if __name__ == '__main__': result = sum(1 for i in takewhile( lambda x: x < 1000000, ((i + 1) ** 3 - i ** 3 for i in count(1))
# This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://san-ss.is-a-geek.com.ar ######################################################################## from CommonFunctions import find_primes_less_than from itertools import count, takewhile primes = find_primes_less_than(int(1000000**0.5)) def is_prime(n): limit = n**0.5 for p in primes: if p > limit: return True if n % p == 0: return False return True if __name__ == '__main__': result = sum(1 for i in takewhile(lambda x: x < 1000000, ((i + 1)**3 - i**3
# but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://wiki.san-ss.com.ar # Visit my blog at http://blog.san-ss.com.ar ######################################################################## from CommonFunctions import find_primes_less_than from itertools import takewhile primes = find_primes_less_than(6 * (10 ** 6)) primes_set = set(primes) def primes_in_range(from_, to_): p_limit = (to_ + 1) ** (0.5) prime_set = set(range(from_, to_ + 1)) for p in takewhile(lambda x: x <= p_limit, primes): mod = from_ % p start_n = from_ + (0 if mod == 0 else p - mod) for i in range(start_n, to_ + 1, p): prime_set.discard(i) return prime_set sum_n = lambda n: n * (n + 1) // 2
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://san-ss.wikidot.com ######################################################################## from CommonFunctions import find_primes_less_than from itertools import dropwhile is_anagram = lambda x, y: sorted(str(x)) == sorted(str(y)) if __name__ == '__main__': primes = find_primes_less_than(10000) primes_greater_1000 = dropwhile(lambda x: x <= 1000, primes) primes = set(primes) found_one = False for base in primes_greater_1000: for increment in range(1, ((10000 - base) // 2)): n1 = base + increment n2 = base + increment * 2 if n1 in primes and n2 in primes and is_anagram( base, n1) and is_anagram(base, n2): if found_one: print("The result is:", str(base) + str(n1) + str(n2)) exit(0) found_one = True
# GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://wiki.san-ss.com.ar # Visit my blog at http://blog.san-ss.com.ar ######################################################################## from CommonFunctions import find_primes_less_than from fractions import Fraction d = {} primes = set(find_primes_less_than(501)) for i in range(1, 501): if i in primes: d[(i, 'P')] = Fraction(2, 3) d[(i, 'N')] = Fraction(1, 3) else: d[(i, 'P')] = Fraction(1, 3) d[(i, 'N')] = Fraction(2, 3) def calc_prob(i, string): if (i, string) in d: return d[(i, string)] if (i == 1): prob = d[(i, string[0])] * calc_prob(i + 1, string[1:]) elif (i == 500):
# GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://wiki.san-ss.com.ar # Visit my blog at http://blog.san-ss.com.ar ######################################################################## from CommonFunctions import find_primes_less_than from fractions import Fraction d = {} primes = set(find_primes_less_than(501)) for i in range(1, 501): if i in primes: d[(i, 'P')] = Fraction(2, 3) d[(i, 'N')] = Fraction(1, 3) else: d[(i, 'P')] = Fraction(1, 3) d[(i, 'N')] = Fraction(2, 3) def calc_prob(i, string): if (i, string) in d: return d[(i, string)] if (i == 1): prob = d[(i, string[0])] * calc_prob(i + 1, string[1:])
# This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. # # You can contact me at [email protected] # Visit my wiki at http://san-ss.wikidot.com ######################################################################## from CommonFunctions import find_primes_less_than from itertools import islice, count primes = set(find_primes_less_than(1000000)) def is_truncable(i): if i < 10: return False tmp = str(i) for x in range(len(tmp)): if (int(tmp[x:]) not in primes) or (int(tmp[:x + 1]) not in primes): return False return True if __name__ == '__main__': result = sum(islice(filter(is_truncable, primes), 11)) print("The result is:", result)
while n >= 10:
result += sum(len(numbers[c]) for c in str(n)) * 2
n = sum(int(c) for c in str(n))
result += sum(len(numbers[c]) for c in str(n)) * 2
return result
def max_clock(n):
global numbers
result = 0
prev_n = 'x' * len(str(n))
while n >= 10:
str_n = 'x' * (len(prev_n) - len(str(n))) + str(n)
result += sum(
len((numbers[a] | numbers[b]) - (numbers[a] & numbers[b]))
for a, b in zip(prev_n, str_n))
prev_n = str(n)
n = sum(int(c) for c in str(n))
str_n = 'x' * (len(prev_n) - len(str(n))) + str(n)
result += sum(
len((numbers[a] | numbers[b]) - (numbers[a] & numbers[b]))
for a, b in zip(prev_n, str_n))
result += sum(len(numbers[a]) for a in str(n))
return result
if __name__ == '__main__':
primes = (x for x in find_primes_less_than(2 * (10**7)) if x > 10**7)
result = sum(sam_clock(x) - max_clock(x) for x in primes)
print("The result is: {0}", result)