def __init__(self, limit):

self.limit = limit

self.triplets = []

def sum(self):

return sum([sum(x) for x in self.triplets])

def find_triplets(self):

# self.triplets = []

pp = mylib.make_primes_sieve_atkin(self.limit)

bb = dict()

r = int(self.limit ** 0.5 // 1)

ss = [x ** 2 for x in pp if x < r]

print(len(pp), "primes, last 10:", sorted(pp)[-10:])

print(len(ss), "squares, last 10:", ss[-10:], "\n")

for a in pp:

print("\033[F\033[K", a, "filtering")

a1 = a + 1

for s in ss:

if s > a1:

bb[a] = (a1, 1)

break

if not a1 % s:

b = a1 // s

if (b - 1) in bb and bb[b - 1][0] != b:

bb[a] = (bb[b - 1][0], a1 // b * bb[b - 1][1])

else:

bb[a] = (b, a1 // b)

break

else:

bb[a] = (a1, 1)

continue

_aaa = dict()

for a in bb:

print("\033[F\033[K", a, 'combining')

b = bb[a][0]

if b not in _aaa:

_aaa[b] = dict()

_aaa[b][a] = round(bb[a][1] ** (1 / 2))

aaa = dict()

n = 0

for b in _aaa:

l = len(_aaa[b])

if l > 1:

print("\033[F\033[K", b, "use elements with len > 1:", l)

aaa[b] = _aaa[b]

n += l * (l - 1) // 2

# else:

# print("\033[F\033[K", k, "remove elements with len = 1")

k = len(aaa)

print("TOTAL", k, "keys to iterate")

print("TOTAL", n, "iterations\n")

bb = sorted(aaa.keys())

k1 = 0

n1 = 0

for b in bb:

k1 += 1

aa = aaa[b]

rr = sorted(aa.keys())

l = len(rr)

print(k1, "/", k, ":", b, l, rr, "\n")

for i in range(0, l):

for j in range(i + 1, l):

n1 += 1

p = rr[i]

q = rr[j]

r = b * aa[p] * aa[q] - 1

if r not in pp:

continue

t = (p, r, q)

self.triplets.append(t)

print("\033[F\033[K", n1, "/", n, t, len(self.triplets))

@staticmethod

def test():

t = Triplets(10 ** 2)

t.find_triplets()

return t.sum() == 1035

@staticmethod

def solve():

t = Triplets(10 ** 8)

t.find_triplets()