def problem124(): checker = primes(save=True,initial=False) unsorted = [(1,1)] for c in generateFactors(100000,checker): unsorted.append((radFromFactors(c),product(c))) # Python already sorts list of tuples as first index first, second index in case of ties # so we use this by adding the elements rad(n) first unsorted.sort() return unsorted[10000-1][1]
def problem87(): checker = primes(save=True,initial=False) seen = [] GOAL = 5*10**7 for c in checker[1:(GOAL - 2**3 - 2**2)**(1/4)]: for b in checker[1:(GOAL - c**4 - 2)**(1/3)]: for a in checker[1:(GOAL - c**4 - b**3)**(1/2)]: seen.append(a**2 + b**3 + c**4) #print(a**2 + b**3 + c**4) return len(set(seen))
def problem104():
c = primes()
memo={0:0, 1:1}
for k, F in enumerate(genLast10Fib()):
if isPandigital(F):
a = top_digits(k+1)
if isPandigital(a):
return k + 1
if k+2 > 329468:
break
def problem179():
GOAL = 10**7
checker = primes(save=True,initial=False)
#primes = rwh_primes2(GOAL//2)
previous = 0
# counting 2
count = 0
d = {1:1}
for n in generateFactors(GOAL+1, checker):
d[product(n)] = sigmaFromFactors(n)
for n in range(1,GOAL):
if d[n] == d[n+1]: count+=1
return count
def problem123(): checker = primes(save=True,initial=False) for n, p in enumerate(checker[0:10**6]): #print(n+1,p) if (n+1) % 2 == 1 and 2*(n+1)*p > 10**10: return n + 1
def problem233(): checker = primes(save=True, initial=False) checker.cleanup() print(numberOfSolutions(checker.factors(2*10000))) print(checker.factors(10000))