def test_consecutive_primes(n2, xs):
# First the values themselves should be primes.
if not all(test_primality(n2 + x) for x in xs):
return False
# There should be no other primes besides those specified in x.
max_x = max(xs)
for x in xrange(xs[0] + 2, max_x, 2):
if x in xs:
continue
if test_primality(n2 + x):
return False
return True
def solve_p130(num, verbose=True):
s = 0
count = 0
# 9 is the first odd composite value.
v = 9
while count < num:
# Check only composite values
if not test_primality(v):
digits = least_repunit(v)
if (v - 1) % digits == 0:
s += v
count += 1
if verbose:
print v
# Only need to consider 1, 3, 7, and 9, so increment by two.
v += 2
# Skip multiples of 5 manually.
if v % 5 == 0:
v += 2
return s
def test_positions(base, swap_digits):
# No digits left to test, simply test primality
if len(swap_digits) == 0:
# If 0 is in the first digit, reject it since it no longer counts.
if base[0] == 0:
return 0, 0
# Convert from a list of digits to a number of values.
val = convert_list_number(base)
if test_primality(val):
return 1, val
else:
return 0, 0
# Test all values for the first digit, recursively try the rest.
first = swap_digits[0]
remain = swap_digits[1:]
count = 0
sum_vals = 0
for possible in range(10):
base[first] = possible
partial_count, partial_sum = test_positions(base, remain)
count += partial_count
sum_vals += partial_sum
return count, sum_vals
def is_prime(v):
return test_primality(v)
def is_prime(x):
return test_primality(x)