def truncatableR2L(p):
coefficient = 10
q = p
while q > 10:
q = p / coefficient
if not prime.isPrime(q):
return False
coefficient *= 10
return True
def diag():
isPrime(10**9) # Sieve init
last = 1
diagNumsCount = 1
primeCountTillNow = 0
for layer in count(1):
sideLength = 2 * layer
for side in range(1, 5):
last += sideLength
if isPrime(last):
primeCountTillNow += 1
diagNumsCount += 1
ratio = primeCountTillNow / diagNumsCount
if layer % 100 == 0:
print("layer: ", layer, ", ratio: ", ratio, ", last: ", last,
", primes: ", primeCountTillNow, ", tot: ", diagNumsCount)
if ratio < 0.1:
return sideLength
def truncatableL2R(p):
coefficient = 10
m = 0
while m < p:
m = p % coefficient
if not prime.isPrime(m):
return False
coefficient *= 10
return True
def main():
ps = primes(10**6)
biggest = 1
for start in range(len(ps)):
acc = 0
nbTerms = 0
if len(ps[start:]) < biggest:
continue
for p in ps[start:]:
nbTerms += 1
acc += p
if acc > 10**6:
continue
if isPrime(acc) and nbTerms > biggest:
biggest = nbTerms
print("prime ", acc, " with ", nbTerms, " terms")
def isCircularPrimes(n):
if n < 20:
return True
q = n
p = 10
w = 1
while True:
if q / p != 0:
w += 1
else:
break
p *= 10
p = 10**(w - 1)
while w > 1:
w -= 1
n = (n % p) * 10 + n / p
if not prime.isPrime(n):
return False
return True
def test(p):
digits = countItems(str(p))
dupDigits = dict(filter(lambda x: x[1] > 1, digits.items()))
for digit in dupDigits.keys():
serie = 0
smallest = 0
for i in range(10):
pStr = str(p)
if i == 0 and pStr[0] == digit:
continue
num = int(pStr.replace(digit, str(i)))
if (isPrime(num)):
print(num)
serie += 1
if smallest == 0:
smallest = num
print(serie)
if serie == 8:
print(smallest)
return True
return False
import sys
from utils import prime
try:
whichPrime = int(sys.argv[1])
except:
sys.exit("Script execution must follow the following format: python problem7.py <whichPrime>")
count = 0
position = 1
while count != whichPrime:
if prime.isPrime(position):
count += 1
position += 1
sys.exit(str(position - 1))
import sys
from utils import prime
try:
startRange = int(sys.argv[1])
endRange = int(sys.argv[2])
except:
sys.exit("Script execution must follow the following format: python problem10.py <startRange> <endRange>")
sum = 0
for x in range(startRange, endRange + 1):
if prime.isPrime(x):
sum += x
sys.exit(str(sum))
def isASquare(n):
for i in range(1, n / 2):
if n == i ** 2:
return True
if i ** 2 > n:
break
return False
def isTwiceASquare(n):
if n == 0: return True
if n == 1 : return False
if n % 2 != 0: return False
q = n / 2
return isASquare(q)
if __name__ == '__main__':
n = 35
while True:
for i in range(n, 0, -1):
if prime.isPrime(i) and isTwiceASquare(n - i):
break
if i == 1:
print('{} {} {}'.format(n, i, n - i))
exit()
n += 2
