def test_trunc_primes(self):
primes = Primes()
assert primes.truncatable(3797)
primes = Primes()
trunc = []
for prime in primes:
if primes.truncatable(prime):
trunc.append(prime)
if len(trunc) == 10:
assert sum(trunc) == 8920
break
def test_factors(self):
primes = Primes()
assert primes.factors(0) == []
assert primes.factors(1) == []
assert primes.factors(2) == [2]
assert primes.factors(6) == [2, 3]
assert primes.factors(8) == [2, 2, 2]
assert primes.factors(29) == [29]
def pe41():
"""
>>> pe41()
7652413
"""
primes = Primes(1000000)
for perm in permutations(range(7, 0, -1)):
n = list_num(perm)
if primes.is_prime(n):
return n
return -1
def generate_code(n, k):
primes = Primes(n + k)
primes_list = primes.primes_list
#primes_list=primes.primes_3mod4()
print(primes_list)
words = gen_words(primes_list[0:k])
primes = primes_list[k:n + k]
print(primes_list)
print(primes)
code = [[legendre_symbol(w, p) for p in primes] for w in words]
return code
def generate_jacobi_code(n, k):
nlog = int(math.log(n, 2))
primes = Primes(nlog + k + 1)
primes_list = primes.primes_list
#primes_list=primes.primes_3mod4()
print(primes_list)
words = gen_words(primes_list[0:k])
primes = primes_list[k:nlog + k]
encoders = gen_words(primes)
print(primes_list)
print(encoders)
code = [[jacoby_symbol(w, m) for m in encoders] for w in words]
return code
def test_primes(self):
primes = Primes()
assert 0 not in primes
assert 1 not in primes
taketen = primes[1:11]
correct = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
taketen = list(taketen)
assert taketen == correct
for x in range(1, 11):
assert primes[x] == correct[x - 1]
assert 104744 not in primes
assert primes[10001] == 104743
itr = iter(primes)
for _ in range(10100):
next(itr)
assert list(primes.countdown(29))[::-1] == correct
def main():
a= Primes(2, 100000, 2000)
p = random.choice(a)
q = random.choice(a)
#print("随机生成两个素数p和q. p=",p," q=",q)
n = p * q
s = (p-1)*(q-1)
#print("The p is ", p)
#print("The q is ", q)
#print("The n(p*q) is ",n)
e = co_prime(s)
#e = 5
#print("根据e和(p-1)*(q-1))互质得到: e=", e)
d = find_d(e,s)
#print("根据(e*d) 模 ((p-1)*(q-1)) 等于 1 得到 d=", d)
#print("公钥: n=",n," e=",e)
#print("私钥: n=",n," d=",d)
pbvk = (n,e,d)
return pbvk
def pe27():
"""
>>> pe27()
(-59231, (-61, 971, 71))
"""
m = (0, 0, 0)
primes = Primes(15000)
for a in range(-999, 1000):
for b in range(max(2, 1 - a), 1000):
n, cnt = 0, 0
while 1:
p = n * (n + a) + b
if primes.is_prime(p):
cnt += 1
else:
break
n += 1
if cnt > m[2]:
m = (a, b, cnt)
return (m[0] * m[1], m)
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Solve project euler 58
Investigate the number of primes
that lie on the diagonals of the spiral grid.
"""
from primes import Primes
primes = Primes(30000)
def pe58(p=0.1):
"""
>>> pe58()
26241
"""
l = 7
ps = 8
d = 49
ds = 13
while ps > p * ds:
l += 2
i = l - 1
ps += primes.is_prime(d + i) + primes.is_prime(
d + 2 * i) + primes.is_prime(d + 3 * i)
d += i << 2
ds += 4
return l
def test_totient(self):
correct = [(2, 1), (3, 2), (4, 2), (5, 4), (6, 2), (7, 6), (8, 4),
(9, 6), (10, 4), (4079147, 4074720)]
primes = Primes()
for (k, v) in correct:
assert primes.totient(k) == v
def primes():
return Primes()
def test_is_circular(self):
primes = Primes()
assert primes.is_circular(2)
assert primes.is_circular(971)
assert not primes.is_circular(999953)
'''
import maths
primesd = maths.primesd(10**6)
primes = [x for x in primesd.keys() if primesd.get(x) is 1]
'''
from primes import Primes
primes = Primes(10**6)
ps = primes.pList()
def Euler_50():
high = 0
for i in range(10):
sums = 0
x = 0
if i % 10000 == 0:
print('new', i)
for j in ps[i:]:
x += 1
sums += j
if sums > 10**6: break
if primes.isPrime(sums):
if x > high:
high = x
maxs = sums
#;print('high:',high,'sum:',sums,'i:',primes.pList(i))
return maxs
if __name__ == '__main__':
print(Euler_50())
def button_handle_random(self, event): # 按钮(随机素数)事件
a = Primes(2, 5000, 1000)
p = random.choice(a)
q = random.choice(a)
self.content_P.set("%s" % p)
self.content_Q.set("%s" % q)
def empty_Primes():
from primes import Primes
new_primes = Primes()
return new_primes
def test_primes_slice():
"""Test method first returns correct slice."""
from primes import Primes
Primes = Primes()
assert Primes.first(20)[-5:] == [53, 59, 61, 67, 71]
def test_consecutive_sum_max(self):
primes = Primes()
assert (2 == primes.consecutive_sum_max(5))
assert (0 == primes.consecutive_sum_max(11))
assert (6 == primes.consecutive_sum_max(41))
def test_prime_80thth_element():
"""Test method first returns correct element."""
from primes import Primes
Primes = Primes()
assert Primes.first(80)[79] == 409
def test_prime_100th_element():
"""Test method first returns correct element."""
from primes import Primes
Primes = Primes()
assert Primes.first(100)[99] == 541
import sys
sys.path.append('C:\\Users\\bob\\comp-sci\\project-euler\\toolkit')
from primes import Primes
p = Primes(1000000)
is_prime = p.is_prime
p_list = p.primes_list
def solve():
most_terms, prime = 0, 0
for terms in range(1, 547):
for i in range(len(p_list) - terms):
p_sum = sum(p_list[i:i+terms])
if p_sum > 1000000:
break
if is_prime(p_sum):
most_terms, prime = terms, p_sum
break
return prime
def setUp(self):
self.primes = Primes(100)
def test_primes_1000th_prime_is_7919(self):
s = Primes(10000)
self.assertEqual(s.first(1000)[-1], 7919)
""" The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ? """ from primes import Primes primes = Primes(10000) print(list(primes.prime_factors((600851475143))))
def test_consecutive_sum_max_length(self):
primes = Primes()
assert primes.consecutive_sum_max_length(50) == (41, 6)
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
What is the smallest odd composite
that cannot be written as the sum of a prime and twice a square?
"""
from primes import Primes
_SQ = [i * i << 1 for i in range(100)]
primes = Primes()
def is_goldbach(n):
res = False
for i in range(100):
t = n - _SQ[i]
if t < 2:
break
if primes.is_prime(t):
res = True
break
return res
def pe46():
"""
>>> pe46()
5777
"""
limit = 10000
import timeit
from triangular import count_factors
from triangular import gen_triangular_number
from primes import Primes
i = 1
while True:
i +=1
pobj = Primes(i)
t = gen_triangular_number(i)
factors = count_factors(pobj, t)
if factors >= 500:
print ("factors", factors, "t", t)
break
#!/usr/bin/python3
'''
Primes generator using Sieve of Eratosthenes
Use -l to limit output or use Ctrl+C to interrupt.
'''
import argparse
import sys
from primes import Primes
argument_parser = argparse.ArgumentParser('Primes generator')
argument_parser.add_argument('-l', dest='limit', type=int, default=None)
limit = argument_parser.parse_args().limit
prime_numbers = Primes()
for prime in prime_numbers:
if limit and prime > limit:
sys.exit()
print(prime)
def ListOfPrimes(num):
listofPrimenumbers = []
for i in range(2, num):
if Primes(i):
listofPrimenumbers.append(i)
return listofPrimenumbers
