def problem231(): n = 20000000 c = 15000000 total = 0 for m in range(n,n-c,-1): print(m) total += sum(factorize(m)) for m in range(c,1,-1): print(-m) total -= sum(factorize(m)) return total
def problem131a(): count = 0 for a in range(1,10**5): a3 = a**3 factorsOfa = factorize(a) div = divisorsFromFactors( factorsOfa + factorsOfa + factorsOfa ) for k in div: n = isSquare(a3 // k) if n and k-n >0 and isPrime(k - n): print(k-n)
def problem168():
power = 1
for n in count(1):
if n > 10**100:
break
if n >= 10**power:
print("reached ", 10**power)
power += 1
if rightShift(n) % n == 0:
if len(set(str(n))) != 1:
print(n,factorize(rightShift(n)))
def problem303():
numbers99 = [i for i in range(999,10000,999)]
n = 999
f = {}
#print(g(2*9))
#print(g(2*99))
return factorize(1111222222222222222222)
while len(numbers99) != 0:
if isMadeOf2(n):
numbersToRemove = []
for k in numbers99:
if n % k == 0:
print(k)
numbersToRemove.append(k)
f[k] = n
if len(numbersToRemove) != 0:
print(factorize(n))
print(gcdd(*numbers99))
for number in numbersToRemove:
numbers99.remove(number)
n += 999
print(f)
def problem131(): seen = 0 for m in count(2): factors = set(factorize(m)) n = m**3 for k in range(0,n,product(factors)**2): if any( k % p != 0 for p in factors): continue if k % product(factors) != 0: print(k) if (n**3 - k**3) % n**2 == 0 and isPrime((n**3 - k**3) // n**2): p = (n**3 - k**3) // n**2 if p > 10**6: return seen print(n, p, k) seen += 1
def problem216():
count = 0
for p in iPrime():
print(jacobi(( p + 1)//2, p))
if p > 100: break
return
for index, n in enumerate(t(100)):
index += 2
#print( 2*(index)**2 -1 , n, isPrime(n), jacobi(( index + 1)//2, index))
if isPrime(n):
count += 1
print("gave a prime ", jacobi(( n + 1)//2, n))
else:
for p in factorize(n):
print("Didn't give a prime", p,jacobi(( p + 1)//2, p))
return count
