def quadratic_primes():
'''Find the product of the coefficients, a and b, for the quadratic expression
n^2 + an + b that produces the maximum number of primes for consecutive values
of n, starting with n=0.'''
primes = [
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,
71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139,
149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223,
227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293,
307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383,
389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463,
467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569,
571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647,
653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743,
751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941,
947, 953, 967, 971, 977, 983, 991, 997
]
max_count = 0
result = (0, 0)
for b in primes:
for a in range(-999, 1000):
n = 0
count = 0
while p3.is_prime(n**2 + a * n + b):
count += 1
n += 1
if max_count < count:
max_count = count
result = (a, b)
return result[0] * result[1]
def primes(max_val):
p = [2]
i = 2
while p[-1]<max_val:
i+=1
if is_prime(i):
p.append(i)
return p[:-1]
def nth_prime(n):
p = []
i = 0
while len(p)<n:
i+=1
if is_prime(i):
p.append(i)
return p[-1]
def sum_prime(num):
'''Return sum of primes < num
>>> sum_prime(2)
2
>>> sum_prime(10)
17
'''
total = 0
for i in range(2, num + 1):
if p3.is_prime(i):
total += i
return total
def primes(num):
'''Return a list of primes < num
>>> primes(2)
[]
>>> primes(3)
[2]
>>> primes(10)
[2, 3, 5, 7]
'''
l = []
for i in range(2, num):
if p3.is_prime(i):
l.append(i)
return l
def ten_thousand_first_prime():
'''Return the 10001st prime'''
count = 1 # 2 is the only even prime, start from 3 after and increment by 2
start = 3
end = 9999
while True:
for i in range(start, end, 2):
if p3.is_prime(i):
count += 1
if count == 10001:
return i
# set the next interval
start = end
end = end + 10000
def circular_primes(num):
'''Return the number of circular primes < num
>>> circular_primes(2)
0
>>> circular_primes(3)
1
>>> circular_primes(100)
13
'''
l = primes(num)
count = 0
for prime in l:
rs = rotations(prime)
for rotation in rs:
if not p3.is_prime(rotation):
break
else:
count += 1
return count
