def rotate(n):
powTen = int(10**(math.floor(math.log(n, 10))))
rotations = []
init = (n % powTen * 10 + n / powTen)
rotations.append(init)
while init != n:
init = (init % powTen * 10 + init / powTen)
rotations.append(init)
return rotations
def getCircularPrimes(primeList):
circularPrimes = [
2,
5,
]
for p in primeList:
rotations = rotate(p)
if all(i % 2 == 1 and i % 5 != 0 for i in rotations):
if all(i in primeList for i in rotations):
for j in rotations:
circularPrimes.append(j)
return circularPrimes
if __name__ == '__main__':
circularPrimes = getCircularPrimes(tools.getPrimes(1000000))
print len(set(circularPrimes))
digits = []
while powTen > 0:
tmp = num / powTen
digits.append(tmp)
num %= powTen
powTen /= 10
return digits
def toNum(tup):
return 1000 * tup[0] + 100 * tup[1] + 10 * tup[2] + tup[3]
if __name__ == '__main__':
primes = sorted(tools.getPrimes(10000))
primes = primes[168:]
candidates = []
done = []
for prime in primes:
prime_perms = []
if prime in done:
continue
else:
digits = getDigits(prime)
for perm in itertools.permutations(digits):
num = toNum(perm)
if num in primes and num not in done:
prime_perms.append(num)
done.append(num)
#33491st import math import tools def rotate(n): powTen = int(10**(math.floor(math.log(n, 10)))) rotations = [] init = (n%powTen*10 + n/powTen) rotations.append(init) while init != n: init = (init%powTen*10 + init/powTen) rotations.append(init) return rotations def getCircularPrimes(primeList): circularPrimes = [2, 5,] for p in primeList: rotations = rotate(p) if all(i%2 == 1 and i%5 != 0 for i in rotations): if all(i in primeList for i in rotations): for j in rotations: circularPrimes.append(j) return circularPrimes if __name__ == '__main__': circularPrimes = getCircularPrimes(tools.getPrimes(1000000)) print len(set(circularPrimes))
def getDigits(num): powTen = 1000 digits = [] while powTen > 0: tmp = num/powTen digits.append(tmp) num %= powTen powTen /= 10 return digits def toNum(tup): return 1000*tup[0] + 100*tup[1] + 10*tup[2] + tup[3] if __name__ == '__main__': primes = sorted(tools.getPrimes(10000)) primes = primes[168:] candidates = [] done = [] for prime in primes: prime_perms = [] if prime in done: continue else: digits = getDigits(prime) for perm in itertools.permutations(digits): num = toNum(perm) if num in primes and num not in done: prime_perms.append(num) done.append(num)
#32461st import tools prime_list = tools.getPrimes(100000) def isPrime(x): index = 0 while prime_list[index] <= x and index < len(prime_list): if prime_list[index] == x: return True index += 1 return False if __name__ == '__main__': max = 0 coefficient_tuple = (0,0) for a in xrange(-999,1000,2): for b in xrange(-999,1000,2): if 1521 + b < a*39: break x = 0 while isPrime(x**2 + a*x + b): x += 1 if x > max: max = x coefficient_tuple = (a,b) print max print coefficient_tuple print coefficient_tuple[0] * coefficient_tuple[1]
import math import tools primes = tools.getPrimes(800000) primes.sort() def is_prime(n): if n == 1: return False if n in primes: return True return False def left_truncatable(n): while n > 0: if not is_prime(n): return False n /= 10 return True def right_truncatable(n): q = 10 while q < n: if not is_prime(n%q): return False q *= 10 return True if __name__ == "__main__": start37 = primes[4:25]