def factorize_trial(n, primes):
"""Factorizing n"""
if miller_rabin(n):
return n
result = []
for p in primes:
while n % p == 0:
result.append(p)
n //= p
if miller_rabin(n):
result.append(n)
break
return result
def A0(n):
for k in xrange(2, 17):
x = repunit(k)
if miller_rabin(x): continue
f = RetFact(x)
if n in f:
return k
return 0
def A0(n):
for k in xrange(2,17):
x = repunit(k)
if miller_rabin(x):continue
f = RetFact(x)
if n in f:
return k
return 0
def PollardRho(n):
if miller_rabin(n):
return n
out = 0
i = 0
xi = random.randint(0,n-1)
xi = 5
k = 2
y = xi
while True:
i = i + 1
xi = ((xi ** 2) + 1) % n
d = gcd(y - xi,n)
if d != 1 and d != n:
if miller_rabin(d):
out = d
break
if i == k:
y = xi
k = 2 * k
return out
def rho(n):
if miller_rabin(n):
return n
def g(x, m):
return (x*x - 1) % m
x = 2
y = 2
d = 1
while d == 1:
x = g(x, n)
y = g(g(y, n), n)
d = gcd(abs(x - y), n)
if d == n:
return False
else:
return d
for i in xrange(2, 9):
x = combinations(l, i)
for p in x:
xx = permutations(p)
for xxx in xx:
#print xxx
qp = ''.join(str(i) for i in xxx)
n = int(qp)
if len(qp) != len(set(qp)): continue
if miller_rabin(n): #IsPrime(n):
#print n
d[i] += [qp]
ctr = 0
#print d[8]
#print
#print len(d[8])
#exit()
a1 = d[1]
b1 = d[2]
c1 = d[3]
d1 = d[4]
e1 = d[5]
for w in xrange(2,10):
d[w]=[]
for i in xrange(2,9):
x = combinations(l,i)
for p in x:
xx = permutations(p)
for xxx in xx:
qp = ''.join(str(i) for i in xxx)
n = int(qp)
if len(qp)!=len(set(qp)):continue
if miller_rabin(n):
#print n
d[i]+= [qp]
ctr=0
a1 = d[1]
b1 = d[2]
c1 = d[3]
d1 = d[4]
e1 = d[5]
f1 = d[6]
g1 = d[7]
h1 = d[8]
zz,zz1,zz2,zz3,zz4,zz5,zz6,zz7='','','','','','','',''
return k
return 0
def A(n, d):
for c in d:
if n in d[c]:
return c
return 0
d = {}
for k in xrange(2, 21):
x = repunit(k)
if miller_rabin(x):
d[k] = [x]
continue
f = RetFact(x)
d[k] = f
print d
print
for n in xrange(3, 20):
if gcd(n, 10) != 1: continue
print n,
print A(n, d)
# 11111111111111111 11111111111111111
# for i in xrange(10**6,10**6+10*3):
for i in xrange(2,9):
x = combinations(l,i)
for p in x:
xx = permutations(p)
for xxx in xx:
#print xxx
qp = ''.join(str(i) for i in xxx)
n = int(qp)
if len(qp)!=len(set(qp)):continue
if miller_rabin(n): #IsPrime(n):
#print n
d[i]+= [qp]
ctr=0
#print d[8]
#print
#print len(d[8])
#exit()
a1 = d[1]
b1 = d[2]
c1 = d[3]
d1 = d[4]
e1 = d[5]
for w in xrange(2, 10):
d[w] = []
for i in xrange(2, 9):
x = combinations(l, i)
for p in x:
xx = permutations(p)
for xxx in xx:
qp = ''.join(str(i) for i in xxx)
n = int(qp)
if len(qp) != len(set(qp)): continue
if miller_rabin(n):
#print n
d[i] += [qp]
ctr = 0
a1 = d[1]
b1 = d[2]
c1 = d[3]
d1 = d[4]
e1 = d[5]
f1 = d[6]
g1 = d[7]
h1 = d[8]
zz, zz1, zz2, zz3, zz4, zz5, zz6, zz7 = '', '', '', '', '', '', '', ''
f = RetFact(x)
if n in f:
return k
return 0
def A(n,d):
for c in d:
if n in d[c]:
return c
return 0
d={}
for k in xrange(2,21):
x = repunit(k)
if miller_rabin(x):
d[k]=[x]
continue
f = RetFact(x)
d[k]=f
print d
print
for n in xrange(3, 20):
if gcd(n,10) != 1: continue
print n,
print A(n,d)
# 11111111111111111 11111111111111111
# for i in xrange(10**6,10**6+10*3):