def longest_chain(x):
record, longest_chain = 0, 0
li = sorted(sieve_of_eratosthenes(x))
ceil = max(li)
for idx, n in enumerate(li):
tmp = n
rest = li[idx + 1:]
if len(rest) < longest_chain:
break
if len(rest) > 0:
for idxx, num in enumerate(rest):
tmp += num
if tmp > ceil:
break
if tmp in rest:
chain = idxx + 2
if chain > longest_chain:
longest_chain = chain
record = tmp
else:
continue
return f'longest chain is {longest_chain} for {record}'
from prob_10 import sieve_of_eratosthenes primes = sorted(sieve_of_eratosthenes(1000000)) truncs = lambda n: [n[:i] for i in range(1,len(n))] + [n[i:] for i in range(1,len(n))] print(sum([n for n in primes[4:] if all([int(m) in primes for m in truncs(str(n))])]))
from prob_10 import sieve_of_eratosthenes
primes = sieve_of_eratosthenes(100000)
find_double_squares = lambda n: [i**2 * 2 for i in range(1, int(n**0.5))]
def find_goldbach(num):
squares = find_double_squares(num)
for p in primes:
if p < num:
for sq in squares:
if p + sq == num:
return True
return False
composites = [i for i in set(range(100000)).difference(primes)
if i % 2 != 0][1:] # omit 1
for n in composites:
if not find_goldbach(n):
print(n)
break
from itertools import combinations
from prob_10 import sieve_of_eratosthenes
same_dig = lambda x, y, z: sorted(str(x)) == sorted(str(y)) == sorted(str(z))
same_dist = lambda x, y, z: x - y == y - z
print([
i for i in combinations(
[k for k in sieve_of_eratosthenes(10000) if k > 1000], r=3)
if same_dist(*i) and same_dig(*i)
])