def encrypt():
# generating a prime numbers list
prime_list = primes(1000)
# choosing two random prime numbers from the list
p = prime_list[random.randint(0, len(prime_list) - 1)]
q = prime_list[random.randint(0, len(prime_list) - 1)]
# n will be the modulus for the public and private keys
n = p * q
# calculating the totient
m = (p - 1) * (q - 1)
# choosing an integer e which is between 1 and the totient.
# e must also be coprime to the totient, so choosing only prime
# numbers inside that range would guarantee that e is coprime.
e_list = primes(1000)
e = e_list[random.randint(0, len(e_list) - 1)]
# choosing a number d such that e*d has a remainder 1 when it is
# divided by m.
for d in range(2, 1000000):
if (e * d) % m == 1:
break
# here, you take the user input and convert each character into
# its appropriate ASCII number
message = input("\nEnter message to encrypt: ")
# the following list will contain all the ASCII numbers of the message
ascii_list = [ord(char) for char in message]
# the following list will contain all the encrypted values of each ASCII number
enc_list = [(a**e) % n for a in ascii_list]
alphabet = "abcdefghijklmnopqrstuvwxyz"
encrypted_string = ""
for encryption in enc_list:
a = random.randint(
13221, 561651616
) # just generating random numbers between key mashed numbers
# concatenating a sequence of numbers and a letter into the final encrypted string
encrypted_string += str(
encryption * a) + "<>" + str(a) + alphabet[encryption % 26] + "<>"
fname = str(e) + " " + str(n) + ".txt"
print(encrypted_string, file=open(fname, 'w'))
print(
"\nYour message has been encrypted in a text file with format 'e n.txt'"
.format(fname))
print("Please keep note of the public keys: e = {0} end n = {1}".format(
e, n))
# check for '__this_folder_is_totally_not_suspicious__' folder
# this folder will contain the private keys ... but .. shhh... you didn't need to know that
if not os.path.isdir("__this_folder_is_totally_not_suspicious__"):
os.mkdir("__this_folder_is_totally_not_suspicious__")
store_priv = open("__this_folder_is_totally_not_suspicious__/" + fname,
"w")
print("{0} {1}".format(d, n), file=store_priv)
def encrypt():
# generating a prime numbers list
prime_list = primes(1000)
# choosing two random prime numbers from the list
p = prime_list[random.randint(0, len(prime_list)-1)]
q = prime_list[random.randint(0, len(prime_list)-1)]
# n will be the modulus for the public and private keys
n = p*q
# calculating the totient
m = (p - 1)*(q - 1)
# choosing an integer e which is between 1 and the totient.
# e must also be coprime to the totient, so choosing only prime
# numbers inside that range would guarantee that e is coprime.
e_list = primes(1000)
e = e_list[random.randint(0, len(e_list)-1)]
# choosing a number d such that e*d has a remainder 1 when it is
# divided by m.
for d in range(2, 1000000):
if (e*d)%m == 1:
break
# here, you take the user input and convert each character into
# its appropriate ASCII number
message = input("\nEnter message to encrypt: ")
# the following list will contain all the ASCII numbers of the message
ascii_list = [ord(char) for char in message]
# the following list will contain all the encrypted values of each ASCII number
enc_list = [(a**e)%n for a in ascii_list]
alphabet = "abcdefghijklmnopqrstuvwxyz"
encrypted_string = ""
for encryption in enc_list:
a = random.randint(13221, 561651616) # just generating random numbers between key mashed numbers
# concatenating a sequence of numbers and a letter into the final encrypted string
encrypted_string += str(encryption * a) + "<>" + str(a) + alphabet[encryption%26] + "<>"
fname = str(e) + " " + str(n) + ".txt"
print(encrypted_string, file=open(fname, 'w'))
print("\nYour message has been encrypted in a text file with format 'e n.txt'".format(fname))
print("Please keep note of the public keys: e = {0} end n = {1}".format(e, n))
# check for '__this_folder_is_totally_not_suspicious__' folder
# this folder will contain the private keys ... but .. shhh... you didn't need to know that
if not os.path.isdir("__this_folder_is_totally_not_suspicious__"):
os.mkdir("__this_folder_is_totally_not_suspicious__")
store_priv = open("__this_folder_is_totally_not_suspicious__/" + fname, "w")
print("{0} {1}".format(d, n), file=store_priv)
def ticket838():
dico = c.get('/bin/hackademy/exam/factoring/trial-division/A')
n = dico['n']
result = []
for p in primes():
if isPrime(n):
result.append(n)
break
if p > math.sqrt(dico['n']):
break
while (n % p == 0):
result.append(p)
n = n//p
print(c.post('/bin/hackademy/exam/factoring',id=dico['id'],factors=result))
def prime_factors(n):
'''Get the prime factors of n.'''
if n < 2:
return []
factors = []
xprimes = primes(n ** 0.5)
while n > 1:
try:
prime = xprimes.pop(0)
while prime:
if n % prime == 0:
xprimes.insert(0, prime)
factors.append(prime)
n /= prime
break
prime = xprimes.pop(0)
except:
return factors + [n]
return factors
from primes import *
def is_truncatable(p):
p = str(p)
for i in range(1, len(p)):
if not (is_prime(int(p[:-i])) and is_prime(int(p[i:]))):
return False
return True
print is_truncatable(97)
count = 0
found = []
for p in primes():
if p > 10:
if is_truncatable(p):
count += 1
found.append(p)
print p
if count == 11:
break
print sum(found)
from math import *
from primes import *
import copy
pSet = set(primes(10000000))
# 9 & 8 can be excluded from search space because
# the sum of digits to 9 and to 8 are multiples of 9 which means the base 10 number
# they form are also divisible by 9
digits = [7,6,5,4,3,2,1]
def findPandigitalPrimes(available, path):
if len(available) == 0:
n = 0
for d in path: n = d + n * 10
if n in pSet:
return n
return None
for d in available:
a2 = copy.copy(available)
a2.remove(d)
path.append(d)
n = findPandigitalPrimes(a2, path)
if n != None: return n
path.pop()
print 'Answer: ' + str(findPandigitalPrimes(digits,[]))
def time_primes(n=10):
return primes(n)
# solution from the website
# Euler 60
from time import time
start = time()
from 60 import primes # Finds all prime numbers less than n
lst=primes(10000)
def isprime(n):
for d in lst:
if n%d==0 and d*d<=n:
return False
if d*d>n:
return True
def p(x,y):
if isprime(int(str(x)+str(y))) and isprime(int(str(y)+str(x))):
return True
else:
return False
ans=(sum((a,b,c,d,e))
for a in lst
for b in lst
if a<b and p(a,b)
for c in lst
if b<c and p(a,c) and p(b,c)
for d in lst
if c<d and p(a,d) and p(b,d) and p(c,d)
for e in lst
if d<e and p(a,e) and p(b,e) and p(c,e) and p(d,e))
return True def euclideTendu(a,b): r=a u=1 v=0 r2=b u2=0 v2=1 while (r2 != 0): q = r//r2 rs = r us = u vs = v r = r2 u = u2 v = v2 r2 = rs - (q*r2) u2 = us - (q*u2) v2 = vs - (q*v2) return [r,u,v] tab = [] for p in primes(): tab.append(p) if len(tab) > 999: break
import bisect
from memoizer import Logger
from primes import *
def inc():
n = 0
yield 0
while 1:
n += 1
if n == 1000:
break
yield n
yield -n
primelist = primes(16000)
def consecutive_primes(a, b):
n = 0
y = n ** 2 + a * n + b
#print "a", a, "b", b, "y", y
while is_prime(y, primelist):
n += 1
y = n ** 2 + a * n + b
#print "-------------------"
#print "a", a, "b", b, "N", n
return n
def foo(a):
ns = map(lambda b: consecutive_primes(a, b), primelist)
n = max(ns)
print "a", a, n, "prime", primelist[ns.index(n)]
from primes import *
pList = primes(10000)
pSet = set(pList)
def test(n):
for p in pList:
if p > n: break;
if ((n-p) / 2) ** 0.5 % 1 == 0: return True
return False
n = 1
while True:
n += 2
if n in pSet: continue
if test(n) is False: break
print 'Answer: ' + str(n)
from primes import *
from digits import *
pList = primes(10000) # need up to 4 digits
pSet = set(pList)
for i in range(len(pList)):
p = pList[i]
if p < 1000: continue
for j in range(i+1, len(pList)):
p2 = pList[j]
p3 = (p2 - p) + p2
if (p2 - p) + p2 in pSet:
if set(toList(p)) == set(toList(p2)) == set(toList(p3)):
print (p, p2, p3)
from primes import *
primesUpTo = 2000000 # 2M
pList = primes(primesUpTo)
pSet = set(pList)
def isPrime(n):
if n < primesUpTo:
return n in pSet
if n > primesUpTo ** 2:
raise Exception("increase prime cache")
# check if there are any prime divisors up to sqrt(n)
checkUpTo = int(n ** 0.5) + 1
for x in pList:
if x > checkUpTo:
return True
if n % x == 0:
return False
# Takes ~ minute to run
sides = 4
n = 1
d = 2 # delta
count = 0
total = 1
while True:
total += sides
for i in range(sides):
