def problem47():
n, count = 6882, 0#2*3*31*37
while count != 4:
primeFactors = prime.primeFactors(n, primes)
if len(primeFactors)==4:
count = count+1
else:
count=0
n=n+1
return n-4
def smallestMultiple(x): allFactors = [] for i in range(2,x): factors = prime.primeFactors(i) factorSet = list(set(allFactors+factors)) newSet = [] for factor in factorSet: newSet += [factor] * max(factors.count(factor),allFactors.count(factor)) allFactors = newSet return allFactors
def phi(n):
assert n > 0
if n != 1:
answer = n
pFactors = prime.primeFactors(n)
pFactors = set(pFactors)
for p in pFactors:
answer *= 1 - 1.0/p
return answer
return 1
def p47():
"""
Keep a running count of the number of factors, wait until 4 in a row with
4 factors are found
"""
prime = gen_primes()
primes = [next(prime)]
i = 2
count = 0
while True:
if (primes[-1] < i):
primes.append(next(prime))
if (len(primeFactors(i, primes)) == 4):
count += 1
else:
count = 0
if (count == 4):
print(i - 3)
break
i += 1
return
import prime
def fourDistinct(ls):
if len(ls) == 4:
return True
else: return False
primes = []
pFlags = prime.sieveAndSet(10000,primes)
consec = 0
for n in range(1000000):
factors = prime.primeFactors(n,primes)[0]
if fourDistinct(factors):
consec += 1
else:
consec = 0
if consec == 4:
print(n-3)
import prime
def fourDistinct(ls):
if len(ls) == 4:
return True
else:
return False
primes = []
pFlags = prime.sieveAndSet(10000, primes)
consec = 0
for n in range(1000000):
factors = prime.primeFactors(n, primes)[0]
if fourDistinct(factors):
consec += 1
else:
consec = 0
if consec == 4:
print(n - 3)
def distPrimes(x):
return len(list(set(prime.primeFactors(x))))
def isSquareFree(n):
factors = prime.primeFactors(n)
return len(factors) == len(set(factors))
def distPrimes(x): return len(list(set(prime.primeFactors(x))))
