def main():
temp = 600851475143
primes = libeuler.primeNumGen(int(math.sqrt(temp)))
for i in primes[::-1]:
if temp % i == 0:
print(i)
break
def main():
result = 0
primes = libeuler.primeNumGen(7654321)
for i in primes[::-1]:
if len(set(str(i))) == len(str(i)) and isPandigital(i):
result = i
break
print(result)
def main():
primes = libeuler.primeNumGen(10000)
primes = [x for x in primes if len(str(x)) == 4]
primeset = set(primes)
used = [ ]
for i in primes:
if (i + 3330) in primeset and (i + 6660) in primeset:
perms = all_perms(str(i))
if str(i+3330) in perms and str(i+6660) in perms:
print(i, i+3330, i+6660)
def main():
i = 1
num = 0
numdivisors = 0
primes = libeuler.primeNumGen(2**16)
while numdivisors < 500:
num += i
i += 1
numdivisors = libeuler.getNumDivisors(num, primes)
print(numdivisors, num)
def main():
primes = libeuler.primeNumGen(10**6)
shortprimes = libeuler.primeNumGen(10**4)
priLen = len(shortprimes)
setprimes = set(primes)
maxprime = primes[-1]
blah = 99999999999
for i in range(priLen):
ii = str(primes[i])
for j in range(i+1, priLen):
jj = str(primes[j])
if not validPair(setprimes, maxprime, ii, jj):
continue
for k in range(j+1, priLen):
kk = str(primes[k])
if (not validPair(setprimes, maxprime, ii, kk) or
not validPair(setprimes, maxprime, jj, kk)):
continue
for l in range(k+1, priLen):
ll = str(primes[l])
if (not validPair(setprimes, maxprime, ii, ll) or
not validPair(setprimes, maxprime, jj, ll) or
not validPair(setprimes, maxprime, kk, ll)):
continue
for m in range(l+1, priLen):
mm = str(primes[m])
if (not validPair(setprimes, maxprime, ii, mm) or
not validPair(setprimes, maxprime, jj, mm) or
not validPair(setprimes, maxprime, kk, mm) or
not validPair(setprimes, maxprime, ll, mm)):
continue
print(ii, jj, kk, ll, mm)
if blah > primes[i] + primes[j] + primes[k] + primes[l] + primes[m]:
blah = primes[i]+primes[j]+primes[k]+primes[l]+primes[m]
print(blah)
def main():
primes = libeuler.primeNumGen(10 ** 6)
setprimes = set(primes)
for prime in primes:
for i in range(10):
temp = 0
if str(i) not in str(prime):
continue
primesToCheck = numsToCheck(prime, i)
for j in primesToCheck:
if int(j) in setprimes and int(j) > prime:
temp += 1
if temp == 7:
print(prime)
return
def main():
primes = libeuler.primeNumGen(10**6)
setprimes = set(primes)
maxconnums = 0
num = 0
for i in range(0, len(primes)):
if maxconnums > len(primes)-i: break
temp = primes[i]
added = 1
for j in range(i+1, len(primes)):
temp += primes[j]
added += 1
if temp > 1000000: break
if temp in setprimes and added > maxconnums:
maxconnums = added
num = temp
print(maxconnums, num)
def main():
primes = libeuler.primeNumGen(10000)
primeset = set(primes)
for i in range(9, 10000, 2): # odd numbers
if i in primeset: continue
x = False
for j in primes:
if j > i: break
for k in range(1,i-j):
temp = j + 2 * k * k
if temp == i:
x = True
break
elif temp > i: break
if x: break
if not x:
print(i)
return
def main():
limit = 10**6
primes = libeuler.primeNumGen(limit)
a = Queue()
b = Queue()
c = Queue()
i = Process(target=worker, args=(range(2, limit+1, 3), primes, a))
j = Process(target=worker, args=(range(3, limit+1, 3), primes, b))
k = Process(target=worker, args=(range(4, limit+1, 3), primes, c))
i.start()
j.start()
k.start()
i.join()
j.join()
k.join()
print(a.get())
print(b.get())
print(c.get())
def main():
numfactors = 0
consecprimes = 0
index = 1
primes = libeuler.primeNumGen(10**6)
primeset = set(primes)
while consecprimes < 4:
if index in primeset:
index += 1
consecprimes = 0
continue
numfactors = len(set(libeuler.primeFactorization(index, primes)))
if numfactors == 4:
consecprimes += 1
else:
consecprimes = 0
index += 1
print(index-4)
def main():
count = 1 #because of 2
primes = libeuler.primeNumGen(1000000)
setprimes = set(primes)
# takes out any primes that have an even digit in them
finalprimes = [ ]
for x in primes:
blah = True
for y in str(x):
if int(y) % 2 == 0:
blah = False
break
if blah:
finalprimes.append(x)
for x in finalprimes:
if iscircularprime(x, setprimes):
count += 1
print(count)
def main():
primes = libeuler.primeNumGen(1000000)
setprimes = set(primes)
result = [ ]
# cant be truncatable
primes.remove(2)
primes.remove(3)
primes.remove(5)
primes.remove(7)
for prime in primes:
truncable = True
for x in range(1, len(str(prime))):
if int(str(prime)[x:]) in setprimes:
if int(str(prime)[:x]) in setprimes:
continue
truncable = False
break
if truncable: result.append(prime)
print(result)
print(sum(result))
def main():
print(sum(libeuler.primeNumGen(2*10**6)))
