Python primes_to_n Examples

Example #1

File: pe_35.py Project: phlip9/project-euler

# Find number of circular primes below 1 million

from pe_utils import primes_to_n, primality_test
from math import log10
from functools import reduce

primes = set(list(primes_to_n(1000000)))
num_primes = len(primes)
circular_primes = set()

def all_rotations(n):
	yield n
	digits_m1 = int(log10(n))
	ten_e_digits = 10**digits_m1
	for i in range(digits_m1):
		n = n / 10 + n % 10 * ten_e_digits
		yield n

def rotation_is_prime(rotations):
	for rotation in rotations:
		if rotation not in primes:
			return False
	return True

for prime in primes:
	if prime not in circular_primes:
		rotations = list(all_rotations(prime))
		if rotation_is_prime(rotations):
			for rotation in rotations:
				circular_primes.add(rotation)

Example #2

# Find number of circular primes below 1 million

from pe_utils import primes_to_n, primality_test
from math import log10
from functools import reduce

primes = set(list(primes_to_n(1000000)))
num_primes = len(primes)
circular_primes = set()


def all_rotations(n):
    yield n
    digits_m1 = int(log10(n))
    ten_e_digits = 10**digits_m1
    for i in range(digits_m1):
        n = n / 10 + n % 10 * ten_e_digits
        yield n


def rotation_is_prime(rotations):
    for rotation in rotations:
        if rotation not in primes:
            return False
    return True


for prime in primes:
    if prime not in circular_primes:
        rotations = list(all_rotations(prime))
        if rotation_is_prime(rotations):

Example #3

# Find the prime generating polynomial of form n^2 + an + b
# where |a| < 1000 & |b| < 1000 and generates the longest array of primes

from pe_utils import prime_sieve, discriminant_bc, complex_quad_polys, primes_to_n

primes = list(prime_sieve(10000))

# only quadratics with disriminant less than 0 can be prime generating
# |b| <= 63
# c cannot be negative, otherwise discriminant would be positive
# 1 <= c <= 1000
# |c| must be prime (1st iteration is always c, and since we're finding primes, c must always be prime)
poly_gen = complex_quad_polys(range(-63, 63 + 1), list(primes_to_n(1000)))


def polynomial(a, b, i):
    return i * i + a * i + b


highest_num_primes = 0
high_ab = None

for ab in poly_gen:
    iterations = 0
    while polynomial(ab[0], ab[1], iterations) in primes:
        iterations += 1

    if iterations > highest_num_primes:
        high_ab = ab
        highest_num_primes = iterations
        print(high_ab, highest_num_primes)

Example #4

File: pe_27.py Project: phlip9/project-euler

# Find the prime generating polynomial of form n^2 + an + b
# where |a| < 1000 & |b| < 1000 and generates the longest array of primes

from pe_utils import prime_sieve, discriminant_bc, complex_quad_polys, primes_to_n

primes = list(prime_sieve(10000))

# only quadratics with disriminant less than 0 can be prime generating
# |b| <= 63
# c cannot be negative, otherwise discriminant would be positive
# 1 <= c <= 1000
# |c| must be prime (1st iteration is always c, and since we're finding primes, c must always be prime)
poly_gen = complex_quad_polys(range(-63, 63 + 1), list(primes_to_n(1000)))

def polynomial(a, b, i):
	return i*i + a*i + b

highest_num_primes = 0
high_ab = None

for ab in poly_gen:
	iterations = 0
	while polynomial(ab[0], ab[1], iterations) in primes:
		iterations += 1

	if iterations > highest_num_primes:
		high_ab = ab
		highest_num_primes = iterations
		print(high_ab, highest_num_primes)

print(highest_num_primes, high_ab)