def co_concat_prime(x, y):
if (x,y) not in known:
if (x + y) % 3 ==0:
known[(x,y)] = False
return False
mx = 10 ** intlen(x)
my = 10 ** intlen(y)
c1 = mx*y + x
c2 = my*x + y
if c1 < c2:
known[(x,y)] = lazy_is_prime(c1) and lazy_is_prime(c2)
else:
known[(x,y)] = lazy_is_prime(c2) and lazy_is_prime(c1)
return known[(x,y)]
def p058():
spiral_count = 0
prime_count = 0
for side_length, spirals in grouped_spirals():
spiral_count += len(spirals)
prime_count += sum((1 for spiral in spirals if lazy_is_prime(spiral)))
if side_length > 2 and prime_count * 10 < spiral_count:
return side_length