def deal(secret, n, k): print secret m = prime.get_primes(secret, 1) for x in prime.get_primes(m[0]*3,n): m.append(x) print 'm: ', m mdash = m[1:k+1] mi = reduce(lambda x,y: x*y, mdash) mdash = m[k+1:n+1] mk = m[0]*reduce(lambda x,y: x*y, mdash) print 'mi: ', mi print 'mk: ', mk if mi>mk: print 'mi > mk: Success' else: print 'mi < mk: Condition failed' M = reduce(lambda x,y: x*y, m) y = secret while(True): a = int(random.random()*100) print 'a: ',a y = secret + a*m[0] print 'y: ',y,' mi:', mi if y < 0 or y > mi: print 'Failure. Trying again!' else: break Y = list() for x in xrange(1,n+1): yi = y % m[x] Y.append(yi) print 'y_'+str(x)+":", yi, 'm_'+str(x)+":", m[x] print 'm0:', m[0]
def generatePrivateKey(self) -> list:
# to obtain random seeds
random.seed(time.time())
# generate the first number of the series
self.sum = random.randint(100, 500)
# private key
key = [self.sum]
# generate the remaining values for private key
for i in range(self.n - 1):
nextnum = random.randint(self.sum + 1, self.sum + 100)
self.sum += nextnum
key.append(nextnum)
# store the modulo required for public key generation
self.modulo = random.randint(self.sum + 130, self.sum + 150)
# get the generator function
prime_handle = prime.get_primes(self.sum + 100)
# get the first prime number : to ensure multiplier and modulo are co prime
self.multiplier = prime_handle.send(None)
# get the inverse of multiplier
self.inverse = gcd.modinv(self.multiplier, self.modulo)
self.private_key = key
# return the private key
return self.private_key
def generate_keys():
# to obtain random seeds
random.seed(time.time())
# generate a random number
startforp = random.randint(100, 200)
# get the generator function
prime_handle = prime.get_primes(startforp)
# get the first prime number
p = prime_handle.send(None)
# put a respectable gap between the two
startforq = startforp + 100
# get the second prime number
q = prime_handle.send(startforq)
# obtain n
n = p * q
# obtain the euler totient of p and q
phi = (p - 1) * (q - 1)
# choosing standard value of e
e = 65537
# Use Extended Euclid's Algorithm to generate the private key
# d = multiplicative_inverse(e, phi)
d = gcd.modinv(e, phi)
# Return public and private keypair
# Public key is (e, n) and private key is (d, n)
return ((e, n), (d, n))
def set_max(max):
global MAX, primes, primes_set
MAX = max
t1 = time.time()
primes = get_primes(MAX)
print time.time()-t1
primes_set = set(primes)
def find_smallest(n):
"""
>>> find_smallest(n)
2520
"""
import prime
import functools
primes = prime.get_primes(n+1)
divisors = list(primes)
for p in primes:
i = 2
while p**i <= n:
divisors.append(p)
i += 1
return functools.reduce(lambda x, y: x*y, divisors)
import prime
primes = prime.get_primes(1000000)
primes_set = set(map(str, primes))
onedigit_primes = [1,2,3,5,7]
onedigit_primes_set = set(map(str, onedigit_primes))
sum = 0
for num in primes:
#for num in [3797]:
if num<10:
continue
num_s = str(num)
if num_s[-1] not in onedigit_primes_set or num_s[0] not in onedigit_primes_set:
continue
for idx in xrange(len(num_s)-1, 0, -1):
if num_s[:idx] not in primes_set:
# print "2", num
break
else:
for idx in xrange(1, len(num_s)):
if num_s[idx:] not in primes_set:
from __future__ import division
from math import sqrt
import prime
MAX=10000000
min_range = int(sqrt(MAX)*0.5)
max_range = int(sqrt(MAX)*1.5)
print "min_range", min_range
print "max_range", max_range
primes = [x for x in prime.get_primes(max_range) if x>min_range]
print primes
def is_perm(a, b):
a_s = str(a)
b_s = str(b)
if len(a_s) != len(b_s):
return False
if set(a_s) != set(b_s):
return False
a_digits = [0]*58
b_digits = [0]*58
for digit in a_s:
""" The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. """ import prime print(sum(prime.get_primes(2000000)))
from prime import get_primes
max_val = 999
target_size = 5
primes = get_primes(max_val)
prime_set = set(primes)
# Returns all valid primes from glob of x (eg 1*3)
def glob_primes(val):
result = set()
if '*' in val:
start = 0
if val[0] == '*':
start = 1
for i in range(start, 10):
x = int(val.replace('*', str(i)))
if x in prime_set:
result.add(x)
else:
val = int(val)
if val in prime_set:
result.add(val)
return result
tried_globs = set()
for prime in primes:
def test_prime_range(self):
primes = [
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
67, 71, 73, 79, 83, 89, 97
]
self.assertEqual(sorted(primes), sorted(get_primes(1, 100)))
from prime import get_primes, prime_factors
max_prime = 300000
primes = get_primes(max_prime)
i = 0
while i < max_prime-3:
if len(prime_factors(i+3, primes)) == 4:
if len(prime_factors(i+2, primes)) == 4:
if len(prime_factors(i+1, primes)) == 4:
if len(prime_factors(i, primes)) == 4:
print(i)
else:
i += 1
else:
i += 2
else:
i += 3
else:
i += 4
def get_indexed_prime(index):
primes = get_primes()
return next(x for i, x in enumerate(primes) if i == index)
import prime primes = prime.get_primes(2000000) print sum(primes)
from prime import get_primes
max_prime = 10000
max_base = 100
primes = set(get_primes(max_prime))
bases = range(1, max_base+1)
sqprimes = set() # Prime + 2*square values
for prime in primes:
for base in bases:
sqprimes.add(prime + (2*(base**2)))
oddcomps = set()
for x in range(9, max(sqprimes)+1, 2):
if x not in primes:
oddcomps.add(x)
print(sorted(oddcomps-sqprimes)[0])
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
lower_n = 0
upper_n = 79
# a must be odd and a in (-1000,1000)
# b must prime and b in [3,997]
upper_a = 1000
upper_b = 1000
upper_prime = upper_n * upper_n + upper_a * upper_n + upper_b
primes = prime.get_primes(upper_prime)
primes_set = set(primes)
best_a = 1
best_b = 41
most_primes_generated = 40
for b in filter(lambda p : p < upper_b, primes):
for a in range(1-upper_a,upper_a,2):
primes_generated = 1
while primes_generated*primes_generated + a*primes_generated + b in primes_set:
primes_generated += 1
if primes_generated > most_primes_generated:
best_a = a
best_b = b
most_primes_generated = primes_generated
import argparse
from sys import argv
from prime import get_primes
primes = None
"""
Verify/Confirm a given number (usually from results.json)
"""
def check(n):
global primes
total = sum([next(primes) ** 2 for _ in range(n)])
print(n, total % n == 0)
if __name__ == '__main__':
primes = get_primes()
parser = argparse.ArgumentParser(description='Verify a number (from results)')
parser.add_argument('n', metavar='N', type=int, default=19,
help='Number to verify')
args = parser.parse_args(argv[1:])
check(args.n)