def get_coin_factors(coinstring):
factorstring = ""
for base in range(2,11):
value = int(coinstring, base)
first_factor_info = next(pyprimes.factorise(value))
factorstring += "{} ".format(first_factor_info[0])
return factorstring.strip()
def worker(s, queue):
ans = s
for b in range(2, 11):
num = base(s, b)
factor = 0
if pyprimes.fermat(num):
ans = 0
break
with timeout(seconds=1):
try:
factor = pyprimes.factorise(num).next()[0]
except:
ans = 0
break
if factor == num:
ans = 0
break
ans = ans + " " + str(factor)
#factors = pyprimes.factors(num)
#if len(factors) == 1:
# ans = 0
# break
#ans = ans +" "+ str(factors[0])
queue.put(ans)
def findEulerTotient(n):
if (pyprimes.isprime(n)):
return n - 1
et = n
for (prime, power) in pyprimes.factorise(n):
et *= (1 - 1.0 / prime)
return et
def order_degree(n):
rtv_o = 1
rtv_d = 1
for p, k in factorise(n):
rtv_o *= p**(2 * k) + p**(2 * k - 1) + p**(2 * k - 2)
rtv_d *= p**k + p**(k - 1)
return rtv_o, rtv_d
def rad(n):
facts = list(factorise(n))
facts = [x[0] for x in facts]
product = 1
for num in facts:
product *= num
return product
def getSumOfSquares(n):
sumOfDivisorSquares = 1
if (pyprimes.isprime(n)):
sumOfDivisorSquares = 1 + n * n
return sumOfDivisorSquares
for (prime, power) in pyprimes.factorise(n):
sumOfDivisorSquares *= (prime**(2 * power + 2) - 1) / (prime**2 - 1)
return sumOfDivisorSquares
def main():
current = 2
while True:
divisors = 1
for factor, count in pyprimes.factorise(sum(range(1, current))):
divisors *= count + 1
if (divisors > 500-1):
print sum(range(1, current))
break
current += 1
def is_valid(self):
self.d = odict()
res = True
for base in range(2, 11):
kb = self.inbase(base)
if pyprimes.isprime(kb):
res = False
break
else:
self.d[base] = pyprimes.factorise(kb).next()[0]
return res
def is_new_record(order, degree):
k = 1
while True:
pks = list(pyprimes.factorise(degree - k))
if len(pks) == 1:
break
k += 1
p, k = pks[0]
q = p**k
o, d = q**2 + q + 1, q + 1
return order > o + (degree - d)
def r_prime_to(num, floor, ceiling): int_num = num num = num+0.0 factors_into = set() for x, exponent in factorise(24): for z in xrange(1,exponent+1): candidate = x**z print floor, candidate/num, ceiling # if candidate/num > floor and candidate < ceiling: # print 'cheese' factors_into.add(candidate) return factors_into
def fast_euler_phi(n, totients): if n == 2: return 1 if n % 2 == 0: if (n / 2) % 2 == 0: return 2 * totients[n / 2] else: return 1 * totients[n / 2] else: if pyprimes.isprime(n): return n-1 else: phi = 1 for (p, a) in pyprimes.factorise(n): phi *= (p ** (a-1)) * (p-1) return phi
def euler_phi(n):
if n == 0: return 0
if n == 1: return 1
if n == 2: return 1
if n % 2 == 0:
if (n / 2) % 2 == 0:
phi_memo[n] = 2 * euler_phi(n / 2)
else:
phi_memo[n] = 1 * euler_phi(n / 2)
else:
if pyprimes.isprime(n):
return n - 1
else:
phi = 1
for (p, a) in pyprimes.factorise(n):
phi *= (p ** (a - 1)) * (p - 1)
phi_memo[n] = phi
return phi_memo[n]
def check_proof_of_work(pow_hash, compact_bits, delta, DONT_CHECK):
#if pow_hash == genesis_pow_hash: return True
target, trailing_zeros = generate_prime_base(pow_hash, compact_bits)
factorization = []
copy = target
if FACTORIZE:
yield "n = "
t = time.time()
for i, j in pyprimes.factorise(target):
yield "({} ^ {}) * ".format(i,j)
copy //= i ** j
factorization.append((i, j))
if time.time() - t > 3: break
yield "{} * 2 ^ {} + {}\n".format(copy, trailing_zeros, delta)
factorization.append((copy, 1))
factorization.append((2, trailing_zeros))
target <<= trailing_zeros
if trailing_zeros < 256:
if delta >= 1 << trailing_zeros:
raise Exception("candidate larger than allowed")
target += delta
if target % 210 != 97:
raise Exception("not valid pow")
def check(remaining):
offset, nchecks_before, nchecks_after = remaining[0]
if not is_prime(target + offset, nchecks_before, True):
raise Exception("n+{0} not prime".format(offset))
if len(remaining) > 1:
yield from check(remaining[1:])
if nchecks_after is not None and not is_prime(target + offset, nchecks_after, False):
raise Exception("n+{0} not prime".format(offset))
yield "n+{0} = {1}\n".format(offset, target + offset)
constellation = [(0, 1, 9), (4, 1, 9), (6, 1, 9), (10, 1, 9), (12, 1, 9), (16, 10, None)]
if DONT_CHECK:
yield [(factorization, delta), [(x[0], target + x[0]) for x in constellation]]
else:
yield from check(constellation)
return True
def order(n):
rtv = n**2
for (p,_) in pyprimes.factorise(n):
rtv *= 1 + 1/p + 1/p**2
return round(rtv)
def get_factors(n):
return pyprimes.factorise(n)
def get_divisors(n):
divisors = [1]
for prime, prime_count in pyprimes.factorise(n):
divisors = [divisor * prime ** count for divisor in divisors for count in range(prime_count + 1)]
return divisors
def degree(n):
rtv = 1
for p, k in pyprimes.factorise(n):
rtv *= p**k + p**(k - 1)
return rtv
def countDivisors(testNum): product = 1 for num, exponent in pyprimes.factorise(testNum): product *= (exponent + 1) return product
#!/usr/bin/python
from pyprimes import factorise
n = 0
while True:
n += 1
a = set(factorise(n))
if len(a) < 4: continue
b = set(factorise(n+1))
if len(b) < 4: continue
c = set(factorise(n+2))
if len(c) < 4: continue
d = set(factorise(n+3))
if len(d) < 4: continue
if len(a & b & c & d) == 0:
print n
break
raise Exception("timing out")
signal.signal(signal.SIGALRM, handler)
print "Case #1:"
for n in xrange(minNum, maxNum + 1, 2):
numList = [int(x) for x in list(bin(n))[2:]]
# if n in BadList:
# continue
signal.alarm(t0)
factList = [] * 0
for B in xrange(2, 11):
num = listAsBase(numList, B)
if pyprimes.isprime(num):
break
try:
facts = pyprimes.factorise(num)
factList.append(next(facts)[0])
except Exception, exc:
break
if len(factList) == 9:
cnt = cnt + 1
print ''.join(map(str,
list(bin(n))[2:])) + ' ' + ' '.join(
map(str, factList))
if cnt >= J:
break
def euler_phi(n):
rtv = n
for p, _ in pyprimes.factorise(n):
rtv *= ( 1 - 1/p )
return round(rtv)
def order(n):
rtv = 1
for p, k in pyprimes.factorise(n):
rtv *= p**(k * 2) + p**(k * 2 - 1) + p**(k * 2 - 2)
return rtv
#!/usr/bin/python
from __future__ import print_function
import re, sys, os
import pyprimes
if __name__ == "__main__":
count = 0
for i in xrange(1, int(sys.argv[1]) - 1):
PFOfi = [prime for prime in pyprimes.factorise(i)]
PFOfiPlus1 = [prime for prime in pyprimes.factorise(i + 1)]
numDivOfi = 1
for (primefactor, power) in PFOfi:
numDivOfi *= (power + 1)
# print(i,numDivOfi)
numDivOfiPlus1 = 1
for (primefactor, power) in PFOfiPlus1:
numDivOfiPlus1 *= (power + 1)
if (numDivOfiPlus1 == numDivOfi):
# print(i,i+1,numDivOfi)
count += 1
print(count)
def degree(n):
rtv = 1
for p, k in pyprimes.factorise(n):
rtv *= p ** k + p ** (k - 1)
return rtv
def order(n):
rtv = n**2
for (p, _) in pyprimes.factorise(n):
rtv *= 1 + 1 / p + 1 / p**2
return round(rtv)
def n_over_phi(n):
rtv = 1
for p, k in factorise(n):
rtv *= p / ( p - 1 )
return rtv
def phi(n):
rtv = 1
for p, k in factorise(n):
rtv *= p**(k-1) * (p-1)
return rtv
def degree(n):
rtv = n
for (p, _) in pyprimes.factorise(n):
rtv *= 1 + 1 / p
return round(rtv)
def degree(n):
rtv = n
for (p,_) in pyprimes.factorise(n):
rtv *= 1 + 1/p
return round(rtv)
def order(n):
rtv = 1
for p, k in pyprimes.factorise(n):
rtv *= p ** (k * 2) + p ** (k * 2 - 1) + p ** (k * 2 - 2)
return rtv
def is_squarefree(n):
for prime, count in factorise(n):
if count >= 2:
return False
return True
