def hamming(smooth,power):
bound = 10**power
'''
prime_list = [] # Generate the prime numbers
for i in range(smooth+1):
if isPrime(i):
prime_list.append(i)
'''
prime_list = sieve(smooth+1)
prime_list.reverse() # Speeds up calculation
exp_list = [] # Determine the maximum exponents can be
for prime in prime_list:
exp_list.append(int(log(bound)/log(prime)))
print exp_list
hcount, count = 0, 1
lim = [0]*len(prime_list) # List to carry exponents
final = hform(prime_list, exp_list, lim, bound, count, hcount)
print '\nThere are %s Hamming numbers of type %s not exceeding 10^%s' % (final, smooth, power)
print '\tFound in %s seconds' % clock()
print '\tThere are %s Primes that include: %s' % (len(prime_list),prime_list)
print '\tThe calculated Exponent limits: %s\n' % exp_list
def hamming(smooth, power):
bound = 10**power
'''
prime_list = [] # Generate the prime numbers
for i in range(smooth+1):
if isPrime(i):
prime_list.append(i)
'''
prime_list = sieve(smooth + 1)
prime_list.reverse() # Speeds up calculation
exp_list = [] # Determine the maximum exponents can be
for prime in prime_list:
exp_list.append(int(log(bound) / log(prime)))
print exp_list
hcount, count = 0, 1
lim = [0] * len(prime_list) # List to carry exponents
final = hform(prime_list, exp_list, lim, bound, count, hcount)
print '\nThere are %s Hamming numbers of type %s not exceeding 10^%s' % (
final, smooth, power)
print '\tFound in %s seconds' % clock()
print '\tThere are %s Primes that include: %s' % (len(prime_list),
prime_list)
print '\tThe calculated Exponent limits: %s\n' % exp_list
def e214(n=25,t = 4*10**7):
p = list(sieve(t))
count = 0
print('start')
mini = 1000
for num in p:
if num>mini:print(num/p[-1],end='\r');mini+=1000
if chain(num)==n:count+=num
return count
def fsandexp(n,pfs=[]):
if n==1:return []
if isprime2(n):return [n]
#p = sieve(int(n**.5)+1)
for i in sieve(int(n**.5)+1):
if n%i==0:
n//=i
pfs+=[i]
#if n==1:return [i]
return [i]+fsandexp(n,pfs)
def fsandexp(n,pfs=[]):
if n==1:return []
if isprime3(n):return [n]
p = list(sieve(int(n**.5)+1))
for i in p:
if n%i==0:
n//=i
pfs+=[i]
#if n==1:return [i]
return [i]+fsandexp(n,pfs)
def fs(n,pfs=[]):
if isprime2(n):return [n]
p = sieve(int(n**.5)+1)
exp = 0
for i in p:
if n%i==0:
while n%i==0:
n//=i
pfs+=[i]
if n==1:return [i]
return [i]+fs(n,pfs)
def fsandexp(n, pfs=[]):
if n == 1:
return []
if isprime2(n):
return [n]
# p = sieve(int(n**.5)+1)
for i in sieve(int(n ** 0.5) + 1):
if n % i == 0:
n //= i
pfs += [i]
# if n==1:return [i]
return [i] + fsandexp(n, pfs)
def test(c=25,n = 4*10**7):
plist = phi(n)
print('pdone')
count = 0
for i in sieve(4*10**7):
j = i
chain = 1
while chain<=25 and j!=1:
j = plist[j]
chain+=1
if chain==25:count+=i
return count
def fs(n, pfs=[]):
if isprime2(n):
return [n]
p = sieve(int(n ** 0.5) + 1)
exp = 0
for i in p:
if n % i == 0:
while n % i == 0:
n //= i
pfs += [i]
if n == 1:
return [i]
return [i] + fs(n, pfs)
def e010(top=2 * 10**6):
return sum(sieve(top))
def e010(top=2*10**6):
return sum(sieve(top))