Example #1
0
def truncatableR2L(p):
    coefficient = 10
    q = p
    while q > 10:
        q = p / coefficient
        if not prime.isPrime(q):
            return False

        coefficient *= 10

    return True
Example #2
0
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
Example #3
0
def truncatableL2R(p):
    coefficient = 10
    m = 0
    while m < p:
        m = p % coefficient
        if not prime.isPrime(m):
            return False

        coefficient *= 10

    return True
Example #4
0
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")
Example #5
0
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
Example #6
0
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
Example #7
0
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))
Example #8
0
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))
Example #9
0
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