def check(n):
if primes.isprime(n): return (n+2)
x=0
while primes.prime(x)<n:
square=math.sqrt((n-primes.prime(x))/2.0)
if square==int(square):
return (n+2)
x+=1
print n
def nextPrime(lastPrimeIndex,depth,prime):
for i in range(lastPrimeIndex-1,depth-1,-1):
prime[NO_NEEDED-1-depth]=primes.prime(i)
if depth==1:
yield prime
else:
yield nextPrime(i, depth-1,prime)
def make_keys(n_primes = 100, pq_bound = 100):
'''
takes: int n
returns: tuples_int pub, prv
'''
n, p, q = 1, 1, 1
prms = primes.prime(n_primes)
while math.log(n, 2) <= 1:
while n < pq_bound:
p, q = np.random.choice(prms, size = 2, replace = False)
n = p * q
print "Key bit length: {}".format(math.log(n, 2))
print "Generated by p: {} and q: {}".format(p, q)
t = (p - 1) * (q - 1) # =: |{k | k < n && (k, n) == 0}|
print "Euler's totient function of {}x{}={}: {}".format(p, q, n, t)
e = t
while primes.gcd(e, t) != 1 or e == 1:
e = int(np.random.uniform(low = 1, high = t))
print "Public key: {}".format(e)
d = primes.inv(e, t)
print "Private key: {}".format(d)
return (n, e), (n, d)
def ok(s, prev=0):
if not s: return 1
v, w = 0, 0
for i,d in enumerate(s):
v = v*10 + d
if v > prev and prime(v):
w += ok(s[i+1:], v)
return w
def prime_handler(conn, addr):
with conn:
while True:
data = conn.recv(BUFSIZE)
if not data:
break
n = int(data)
p = prime(n)
conn.sendall(str(p).encode() + b'\n')
def find():
primes = primes_list(10**4)
for length in xrange(1000, 0, -1):
first = 0
while True:
summ = sum(primes[first:first+length])
# print summ
if summ >= 10**6: break
if prime(summ): return summ
first += 1
#!/usr/bin/env python2
import itertools
import primes
def conjecture(n):
for i in xrange(int((n / 2) ** 0.5), 0, -1):
if primes.prime(n - 2 * i ** 2):
return True
return False
for number in itertools.count(33, 2):
if primes.prime(number):
continue
if not conjecture(number):
break
print "result: %s" % number
import primes
s = [primes.prime(x) for x in range(50)]
def find(target):
ways = [1]+[0]*target
for s_i in range(1,target):
if s_i < target:
for i in range(s_i,target+1):
ways[i] += ways[i - s_i]
if (ways[s_i]+1)%10**6==0:
return s_i+1
print find(10**6)
from primes import is_prime as prime
p = [
x for x in range(1000, 10000)
if prime(x) and prime(x + 3330) and prime(x + 2 * 3330)
]
def isperm(n1, n2):
return sorted(list(str(n1))) == sorted(list(str(n2)))
def isperml(n):
n1 = sorted(list(str(n[0])))
for i in n:
if n1 != sorted(list(str(i))):
return False
return True
for i in p:
if isperml([i, i + 3330, i + 2 * 3330]):
print(str(i) + str(i + 3330) + str(i + 2 * 3330))
from primes import is_prime as prime
p = [x for x in range(1000, 10000) if prime(x) and prime(x + 3330) and prime(x + 2*3330)]
def isperm(n1, n2):
return sorted(list(str(n1))) == sorted(list(str(n2)))
def isperml(n):
n1 = sorted(list(str(n[0])))
for i in n:
if n1 != sorted(list(str(i))):
return False
return True
for i in p:
if isperml([i, i+3330, i+2*3330]):
print(str(i) + str(i+3330) + str(i + 2*3330))
# list2=list(prime)
# count=0
# for k in range(10):
# list2[i+1]=list2[j]=k
# if primes.isprime(listToNum(list2)) and listToNum(list2)>999:
# count+=1
# if count==Amount:
# print listToNum(prime)
# contin=0
# x+=1
##for 3 digits
contin=1
x=25
while contin:
prime=[int(i) for i in str(primes.prime(x))]
for i in range(len(prime)-2):
for j in range(i+2):
for jj in range(j+1):
# if jj==0:
# am=Amount+1
# else
list2=list(prime)
count=0
for k in range(10):
list2[i+2]=list2[j+1]=list2[jj]=k
if primes.isprime(listToNum(list2)) and list2[0]!=0:
count+=1
if count==Amount:
print listToNum(prime)
import time
startTime=time.clock()
import primes
n=4
count=0
sum =0
tprimes=[]
while count < 1000000000000000:
primeList=[int(x) for x in str(primes.prime(n))]
good=1
for x in range(1,len(primeList)):
primeL=0
primeR=0
for i in range(len(primeList)-x):
# print primeList
primeL+=(10**(len(primeList)-x-i-1))*primeList[x+i]
primeR+=(10**(len(primeList)-x-i-1))*primeList[i]
# print primeR
if not (primes.isprime(primeL) and primes.isprime(primeR)):
good=0
break
if good:
tprimes.append(primes.prime(n))
count +=1
sum += primes.prime(n)
print tprimes
print sum
from primes import initpoulet, prime
initpoulet()
add = (1, 3, 7, 9, 13, 27)
S = 10
for n in range(11, 150000000):
if n%100000==0: print(n, S)
if all(prime(n*n+a) for a in add): S += n
print(S)
#print(list(prime(n*n+a) for a in add))
def isPerm(x,y):
x = str(x)
y = str(y)
if len(x)!=len(y):
return False
for ch in x:
if x.count(ch)!=y.count(ch):
return False
return True
maxim = 10**7
minNOverPhy = 10**9
x=2
while primes.prime(x)<maxim:
for y in range(1,x):
if primes.prime(y)*primes.prime(x) > maxim:
break
nOverPhy = float(primes.prime(x)*primes.prime(y))/float((primes.prime(x)-1)*(primes.prime(y) -1))
if minNOverPhy > nOverPhy:
if isPerm(primes.prime(y)*primes.prime(x),(primes.prime(x)-1)*(primes.prime(y) -1) ):
minNOverPhy = nOverPhy
print primes.prime(y)*primes.prime(x), nOverPhy
x+=1
def conjecture(n):
for i in xrange(int((n / 2) ** 0.5), 0, -1):
if primes.prime(n - 2 * i ** 2):
return True
return False
import time
import primes
startTime=time.clock()
n=0
MAX=10**6
noPrimes=0
x=0
while primes.prime(x)<MAX/2:
sum=primes.prime(x)
n=1
while sum<MAX:
sum+=primes.prime(x+n)
n+=1
if primes.isprime(sum):
if n>noPrimes:
noPrimes=n
print noPrimes
print sum
x+=1
endTime=time.clock()
print endTime-startTime
# project euler 07 from primes import prime print prime(10001)