def prime(k):
while True:
q = Prime.prime(k)
p = 2*q+1
test = Prime.miller(p, 100)
if test:
return p
def get_RSAKey():
RSAKey = {}
start = time.perf_counter()
prime_arr = Prime.get_rand_prime_arr(2)
p = prime_arr[0]
q = prime_arr[1]
while p == q:
q = random.choice(prime_arr)
end = time.perf_counter()
n = p * q
s = (p - 1) * (q - 1)
a = 65537
b = Prime.mod_inverse(a, s)
print("随机生成的素数p =", p)
print("随机生成的素数q =", q)
print('素数生成的时间为：', end - start, 's')
print("n = pq =", n)
print("利用Euclidean算法生成的私钥a =", a)
print("利用扩展Euclidean算法生成的公钥b =", b)
puk = [n, a]
prk = [n, b]
RSAKey['puk'] = puk
RSAKey['prk'] = prk
return RSAKey
def procgrid3d_to_2d(pex, pey, pez):
p = Prime()
p1 = p.factorize(pex)
p2 = p.factorize(pey)
p3 = p.factorize(pez)
ptot = sorted(p1 + p2 + p3, reverse=True)
nprow = 1
npcol = 1
for i in range(len(ptot) / 2):
npcol *= ptot[2 * i]
nprow *= ptot[2 * i + 1]
if (len(ptot) - len(ptot) / 2 * 2 == 1):
npcol *= ptot[len(ptot) - 1]
return nprow, npcol
def SetMod(self, mod):
# Set self.mod
# self.mod should be a prime
if not isinstance(mod, int):
raise Error.ModTypeError
if (not Prime.IsPrime(mod)) and mod != 0:
raise Error.ModValueError
self.mod = mod
self._Mod()
def count_perm(n, max_sub, res = {(0,0):1}):
if (n,max_sub) in res:
return res[(n,max_sub)]
p = 0
for i in Prime.primesLessThan(max_sub):
c = count_perm(n - i,min(i,n-i))
p += c
res[(n,max_sub)] = p
return p
def generateRsaKey(size=1024, e=65537):
"Tạo khoá RSA theo PKCS#1 với kích thước mặc định là 1024-bits"
d = 1
while True:
p = Prime.getPrime(size)
q = Prime.getPrime(size)
if RsaMath.gcd((p - 1), e) == 1 and RsaMath.gcd((q - 1), e) == 1:
break
n = p * q
lam_da = ((p - 1) * (q - 1)) / RsaMath.gcd((p - 1), (q - 1))
while d < 2**(size / 2):
d = RsaMath.mod_inverse(e, lam_da)
publicKey = (n, e)
privateKey = (n, d)
return privateKey, publicKey
def get_RSAKey():
RSAKey = {}
prime_arr = Prime.get_rand_prime_arr(2)
p = prime_arr[0]
q = prime_arr[1]
while p == q:
q = random.choice(prime_arr)
n = p * q
s = (p - 1) * (q - 1)
e = 65537
d = Prime.mod_inverse(e, s)
print "p = ", p, ",q = ", q
print "n = ", n
print "e = ", e, ",d = ", d
puk = [n, e]
prk = [n, d]
RSAKey['puk'] = puk
RSAKey['prk'] = prk
return RSAKey
def test_prime(self):
self.assertEqual(Prime.is_prime(3), True)
print(Prime.is_prime(3))
self.assertEqual(Prime.is_prime(19), True)
print(Prime.is_prime(19))
self.assertEqual(Prime.is_prime(12), False)
print(Prime.is_prime(12))
def prime_factor(num):
import Prime
prime_factor_list = []
factor = 2
while num != 1:
if not Prime.prime(factor) :
factor += 1
continue
if num % factor != 0:
factor += 1
continue
else:
num = num / factor
prime_factor_list.append(factor)
return prime_factor_list
class PrimeTest(unittest.TestCase): def setUp(self): self.prime = Prime() def test_number_less_than_zero_not_prime(self): self.assertFalse(self.prime.isPrime(-1)) def test_1_is_not_prime(self): self.assertFalse(self.prime.isPrime(1)) def test_2_is_prime(self): self.assertTrue(self.prime.isPrime(2)) def test_4_is_not_prime(self): self.assertFalse(self.prime.isPrime(4)) def test_5_is_prime(self): self.assertTrue(self.prime.isPrime(5)) def test_massive_number_is_prime(self): self.assertTrue(self.prime.isPrime(1066340417491710595814572169)) def test_massive_even_number_is_not_prime(self): self.assertFalse(self.prime.isPrime(1066340417491710595814572168))
class PrimeTest(unittest.TestCase):
def setUp(self):
self.prime = Prime()
def test_number_less_than_zero_not_prime(self):
self.assertFalse(self.prime.isPrime(-1))
def test_1_is_not_prime(self):
self.assertFalse(self.prime.isPrime(1))
def test_2_is_prime(self):
self.assertTrue(self.prime.isPrime(2))
def test_4_is_not_prime(self):
self.assertFalse(self.prime.isPrime(4))
def test_5_is_prime(self):
self.assertTrue(self.prime.isPrime(5))
def test_massive_number_is_prime(self):
self.assertTrue(self.prime.isPrime(1066340417491710595814572169))
def test_massive_even_number_is_not_prime(self):
self.assertFalse(self.prime.isPrime(1066340417491710595814572168))
import Prime
x = int(input("Enter number of elements: "))
Arr = list()
Sum = 0
for i in range(x):
print("Enter number", (i + 1))
no = int(input())
if Prime.ChkPrime(no) is True:
Sum = Sum + no
Arr.append((no))
print(Arr)
print("Addition of Prime numbers in the List is ", Sum)
import Prime
from itertools import permutations
max_prime = 10000000
ps = set(Prime.prime_seive(max_prime))
done = False
for p in Prime.primes:
pstr = str(p)
for d in set(pstr):
family = []
for i in "0123456789":
f = int(pstr.replace(d,i))
if not len(str(f)) == len(pstr):
continue
if f in ps:
family.append(f)
if len(family) == 8:
done = True
print family
break
if done : break
import Prime Prime.prime_seive(100000) triangle = 1 i = 1 while Prime.factor(triangle).getNdivisors() < 500: i += 1 triangle += i print triangle
def setUp(self): self.prime = Prime()
for b in np.arange(1,10, dtype = float):
if a == b : continue
if (i*10+a)/(i*10+b) == a/b and (i*10+a)/(i*10+b) < 1:
print (i*10+a),'/',(i*10+b)
numerators.append(i*10+a)
denominators.append(i*10+b)
if (i+a*10)/(i*10+b) == a/b and (i+a*10)/(i*10+b) < 1:
print (i+a*10),'/',(i*10+b)
numerators.append(i+a*10)
denominators.append(i*10+b)
if (i+a*10)/(i+b*10) == a/b and (i+a*10)/(i+b*10) < 1:
print (i+a*10),'/',(i+b*10)
numerators.append(i+a*10)
denominators.append(i+b*10)
if (i*10+a)/(i+b*10) == a/b and (i*10+a)/(i+b*10) < 1:
print (i*10+a),'/',(i+b*10)
numerators.append(i*10+a)
denominators.append(i+b*10)
top = int(np.prod(numerators))
bot = int(np.prod(denominators))
Prime.prime_seive(max(top,bot))
pt = Prime.primeFactors(top)
pb = Prime.primeFactors(bot)
gcd = pt.GCD(pb).getValue()
print top,bot,gcd
print top/gcd, bot/gcd
import Prime
from Tools import pandigitals
max_pan = 0
# Note: for n=8,9 all pandigitals are divisible by 9
primeset = set(Prime.prime_seive(int(1e7)))
for i in [7,6,5,4,3,2,1]:
for p in pandigitals(i):
if p in primeset:
max_pan = max(p,max_pan)
if max_pan:
print max_pan
break
import Prime
primeset = set(Prime.prime_seive(999999))
total = 0
for p in primeset:
#left
pstr = str(p)
if len(pstr) == 1 : continue
truncatable = True
for i in range(1,len(pstr)):
if not int(pstr[-i:]) in primeset : truncatable = False
if not int(pstr[:i]) in primeset : truncatable = False
if truncatable:
print p
total += p
print total
import Prime
n = 1000000
primeset = set(Prime.prime_seive(n))
total = 0
for max_n,p in enumerate(Prime.primes):
total += p
if total > n:
break
l = max_n
lb = 5
while l > lb:
for i in range(Prime.n_primes - l + 1):
s = sum(Prime.primes[i:i+l])
if s > n :
break
if sum(Prime.primes[i:i+l]) in primeset:
print l,Prime.primes[i:i+l],sum(Prime.primes[i:i+l])
l = lb
break
l -= 1
import Prime
def quad_prime(a,b,prime_set):
n = 0
x = n**2 + a*n + b
while x in prime_set:
x = n**2 + a*n + b
yield x
n+=1
Prime.prime_seive(100000)
prime_set = set(Prime.primes)
maximum = (0, 0, 0)
for b in Prime.primes:
length = 0
if b > 1000:
break
for a in xrange( 1-b, 1000 ):
l = len([p for p in quad_prime(a,b,prime_set) ] )
maximum = max(maximum,(l,a,b))
print maximum, maximum[1]*maximum[2]
import Prime as p
primeset = set(p.prime_seive(9999))
def is_permutation(one,two):
return sorted(str(one)) == sorted(str(two))
for i in range(p.n_primes):
if p.primes[i] < 1000 : continue
for j in range(i+1,p.n_primes):
if p.primes[j] < 1000 : continue
if not is_permutation(p.primes[i], p.primes[j]):
continue
third = 2*p.primes[j] - p.primes[i]
if third in primeset and is_permutation(p.primes[j],third):
print p.primes[i], p.primes[j],third
import Prime print [p for p in Prime.getNPrimes(10001)][-1]
def encryption(plaintext, puk):
return Prime.quick_pow_mod(plaintext, puk[1], puk[0])
## EMIRP ## ## challenge #67 (easy) ## http://www.reddit.com/r/dailyprogrammer/comments/vfylp/6222012_challenge_68_easy/ ## ## ## [email protected] ## import Prime num = int(raw_input("Enter a number: ")) emirp_list = [] for i in xrange(10, num + 1): if Prime.prime(i): temp = int(str(i)[::-1]) if Prime.prime(temp) and i != temp: emirp_list.append(str(i)) print ", ".join(emirp_list)
def is_right(five):
for p1, p2 in itertools.permutations(five, 2):
if Prime.is_prime(str(p1) + str(p2)) == False:
return False
return True
import Prime
from collections import deque
primeset = set(Prime.prime_seive(1000000))
circulars = set()
for p in primeset:
strp = deque(str(p))
cycles = set()
isCircular = True
for i in range(len(strp)):
strp.rotate(1)
i = int(''.join(map(str, strp)))
if i in primeset:
cycles.add(i)
else:
isCircular = False
if isCircular:
circulars = circulars | cycles
print (circulars, len(circulars))
## EMIRP ## ## challenge #67 (easy) ## http://www.reddit.com/r/dailyprogrammer/comments/vfylp/6222012_challenge_68_easy/ ## ## ## [email protected] ## import Prime num = int(raw_input("Enter a number: ")) emirp_list = [] for i in xrange(10,num+1): if Prime.prime(i): temp = int(str(i)[::-1]) if Prime.prime(temp) and i != temp: emirp_list.append(str(i)) print ", ".join(emirp_list)
def decryption(ciphertext, prk):
return Prime.quick_pow_mod(ciphertext, prk[1], prk[0])
def __init__(self, p, a, k):
self.p = p
self.a = a
self.k = k
self.alpha = Prime.primitiveRoot(p)
self.beta = power(self.alpha, a, p)
import Tools import Prime n = 10**7 Prime.prime_seive(n) print min( [ (n/float(t),n,t) for n,t in Prime.totient(n) if Tools.is_perm(n,t) ])
import Prime from time import time s = time() print sum(Prime.prime_seive(2000000)) print time() - s
import math import Prime n = 600851475143 print Prime.factor(n)
from ElGamal import ElGamal
from base26Cipher import Encrypt
import Prime
from random import randint
# f = open('input.txt')
# np = int(f.readline())
# na = int(f.readline())
# nk = int(f.readline())
# base = f.readline()
base = 'Dexuatcachlyxahoivoinhomdiaphuongnguycocao'
p = 10**99 + 289
a = 10**59 + 1
k = 10**63 + 2
alpha = Prime.primitiveRoot(p)
print(alpha)
# p = Prime.randomPrime(np)
# a = randint(10 ** (na - 1), 10 ** na - 1)
# k = randint(10 ** (nk - 1), 10 ** nk - 1)
# alpha = Prime.primitiveRoot(p)
x = Encrypt(base) % p
print(x)
elGamal = ElGamal(p, a, k)
print(elGamal.beta)
y1, y2 = elGamal.enCode(x)
print((y1, y2))
print(elGamal.deCode(y1, y2))
res = a*1000000 + b
elif b > 10000:
res = a*100000 + b
elif b > 1000:
res = a*10000 + b
elif b > 100:
res = a*1000 + b
elif b > 10:
res = a*100 + b
else:
res = a*10 + b
return res
max_n = 99999999
Prime.prime_seive(max_n)
prime_set = set(Prime.primes)
pairs = {}
print "Making pairs"
ttotal = 0
for i in xrange(Prime.n_primes):
p1 = Prime.primes[i]
for j in xrange(i+1, Prime.n_primes):
ttotal += 1
p2 = Prime.primes[j]
#if Prime.isPrime(cat_ints(p1,p2)) and Prime.isPrime(cat_ints(p2,p1)):
new_p1 = cat_ints(p1,p2)
if new_p1 in prime_set:
new_p2 = cat_ints(p2,p1)
if new_p2 in prime_set :
import Prime
if __name__ == '__main__':
primes = set(Prime.primes)
diags = [1]
nom = 0
denom = 1
for i in range(1, 1000000):
d = i * 2
denom += 4
for j in range(4):
diags.append(diags[-1] + d)
for num in diags[-4:]:
if Prime.is_prime(num) == True:
nom += 1
#print nom, denom
if float(nom) / float(denom) < 0.1:
print d + 1
break
import Prime
#print('Эратосфен в ', Prime2.print_PM_by_Roma(10000, False) / Prime2.print_PM(10000, False), ' раз быстрее')
print(Prime.print_PM(10000, False))
#!/usr/bin/python2
import Prime
import math
def corners(max_n):
for n in xrange(1,max_n+1):
odd = 2*n+1
d = 2*n
for i in xrange(odd**2 - 3*d, odd**2+1, d):
yield i
n = 13500
Prime.prime_seive((2*n+1)**2)
iprime = 0
n_primes = 0.
total = 0.
for c in corners(n):
for i in xrange(iprime,Prime.n_primes):
if Prime.primes[i] == c:
n_primes += 1.
break
elif Prime.primes[i] > c:
break
iprime = i
#pf = Prime.primeFactors(c)
#if Prime.primeFactors(c).isPrime():
#n_primes += 1.
total += 1.
import Prime
Prime.method("")
def decryption(secret, prk):
return Prime.quick_pow_mod(secret, prk[1], prk[0])
def setUp(self):
self.prime = Prime()
def encryption(message, puk):
return Prime.quick_pow_mod(message, puk[1], puk[0])
from Prime import *
from Happy import *
Happy().happyFile()
Prime().primeFile()
overlap = []
happy = open("happy.txt")
prime = open("prime.txt")
happylist = happy.read().split()
primelist = prime.read().split()
for h in happylist:
for p in primelist:
if h == p:
overlap.append(h)
print("The overlapping values in happy numbers and prime numbers are ")
print(", ".join(overlap))
print("The count of overlapping values ranging from 1 to 1000 are",
len(overlap))
import Prime as p
import Reverse as r
for num in range(1, 100):
if (p.isPrime(num)):
revNum = r.getReverse(num)
if (revNum == num): continue
if (p.isPrime(revNum)): print(num)
import numpy as np
import Prime
import matplotlib.pyplot as plt
import streamlit as st
x = st.slider('Select a value', 2, 10000)
Choose = st.radio("With Prime or without", ('Prime', 'Odd', 'All'))
Prime = np.array(Prime.PrimeNum(2, x))
if Choose == 'Prime':
In = Prime
elif Choose == 'Odd':
In = np.arange(start=1, stop=x, step=2)
elif Choose == 'All':
In = np.arange(start=1, stop=x, step=1)
Output = []
for i in In:
Temp = np.binary_repr(i)
TempReverse = Temp[::-1]
T1 = int(Temp, 2)
T2 = int(TempReverse, 2)
Output.append(T2 - T1)
if Choose == 'Prime':
plt.scatter(In, Output, c="blue")
elif Choose == 'Odd':
plt.scatter(In, Output, c="red")
elif Choose == 'All':
plt.scatter(In, Output, c="orange")
import math import Prime lcm = Prime.factor(2) for i in range(3,21): lcm = lcm.LCM(Prime.factor(i)) print reduce(lambda x, y: x*y, lcm.getlist())
import Prime n = 1000000 Prime.prime_seive(n) print max([ (n/float(t),n) for n,t in Prime.totient(n) ])
