def solution():
"""
Bryukh's solution
>>> solution()
[148748178147, 296962999629]
"""
res = []
pr_list = eratosthenes(10000)
pr_list = pr_list[pr_list.index(1009):]
while pr_list:
pr = pr_list[0]
pr_per = [
int(''.join(var)) for var in permutations(str(pr))
if int(''.join(var)) in pr_list
]
pr_per = sorted(list(set(pr_per)))
for x in pr_per:
pr_list.remove(x)
if len(set(pr_per)) < 3:
continue
for i in xrange(len(pr_per) - 2):
for j in xrange(i + 1, len(pr_per) - 1):
third = pr_per[j] + (pr_per[j] - pr_per[i])
if third in pr_per:
res.append(pr_per[i] * (10**8) + pr_per[j] * (10**4) +
third)
return res
def solution2(value=CONST):
"""
Bryukh's solution
four time calculation in one
>>> solution(2)
14
>>> solution(3)
644
"""
def count_div(numb, lst):
res = 0
for pr in lst:
if not numb % pr:
res += 1
if pr > numb/2:
if not res:
res = 1
break
return res
pr_list = eratosthenes(100000)
x = 10
x_divisors = [0] * value
for i in range(value):
x_divisors[i] = count_div(x+i, pr_list)
while True:
if all([xd==value for xd in x_divisors]):
break
x += 1
x_divisors = x_divisors[1:] + [count_div(x+value-1, pr_list)]
return x
def solution():
"""
Bryukh's solution
"""
prime_list = eratosthenes(1000000)
res = []
for pr in prime_list:
if (all([(int(str(pr)[i:]) in prime_list and
int(str(pr)[:i+1]) in prime_list)
for i in xrange(len(str(pr)))])):
res.append(pr)
return sum(res[-11:])
def solution():
"""
Bryukh's solution
"""
prime_list = eratosthenes(1000000)
res = []
for pr in prime_list:
if (all([(int(str(pr)[i:]) in prime_list
and int(str(pr)[:i + 1]) in prime_list)
for i in xrange(len(str(pr)))])):
res.append(pr)
return sum(res[-11:])
def solution(value=CONST):
"""
Bryukh's solution
n/φ(n) = (1-1/p1)(1-1/p2)...
so maximum is maximum prime divisors
>>> solution()
510510
"""
prlist = eratosthenes(100)
res = 1
for pr in prlist:
if res * pr > value:
return res
res *= pr
def solution(value=CONST):
"""
Bryukh's solution
n/φ(n) = (1-1/p1)(1-1/p2)...
so maximum is maximum prime divisors
>>> solution()
510510
"""
prlist = eratosthenes(100)
res = 1
for pr in prlist:
if res*pr > value:
return res
res *= pr
def solution(value=CONST):
"""
Bryukh's solution
We can check only 3 repeat numbers
>>> solution()
"""
prime_lst = [pr for pr in eratosthenes(999999) if repeating_digit(pr, 3)]
for prime in prime_lst:
templates = find_template(prime, 3)
#print prime, template
for temp in templates:
gen_lst = generate_numb(prime, temp)
count = sum([1 for gen in gen_lst if gen in prime_lst])
if count >= 8:
return prime
def solution(value=CONST):
"""
Bryukh's solution
We can check only 3 repeat numbers
>>> solution()
"""
prime_lst = [pr for pr in eratosthenes(999999) if repeating_digit(pr, 3)]
for prime in prime_lst:
templates = find_template(prime, 3)
#print prime, template
for temp in templates:
gen_lst = generate_numb(prime, temp)
count = sum([1 for gen in gen_lst if gen in prime_lst])
if count >= 8:
return prime
def solution(max_value=CONST):
"""
Bryukh's solution
"""
prime_lst = eratosthenes(max_value)
res = 0
len_res = 0
for start in xrange(10):
temp = 0
for i in prime_lst[start:]:
temp += i
if temp > max_value:
break
if temp in prime_lst:
if i - start > len_res:
len_res = i - start
res = temp
return res
def solution():
"""
Bryukh's solution
>>> solution()
5777
"""
n = 7
prime_lst = eratosthenes(100000)
while True:
n += 2
if n in prime_lst:
continue
for pr in prime_lst:
if n < pr:
return n
diff = n - pr
if not diff % 2 and sqrt(diff // 2) == int(sqrt(diff // 2)):
break
def solution():
"""
Bryukh's solution
>>> solution()
5777
"""
n = 7
prime_lst = eratosthenes(100000)
while True:
n += 2
if n in prime_lst:
continue
for pr in prime_lst:
if n < pr:
return n
diff = n - pr
if not diff % 2 and sqrt(diff//2) == int(sqrt(diff//2)):
break
def solution(max_value=CONST):
"""
Bryukh's solution
"""
prime_lst = eratosthenes(max_value)
res = 0
len_res = 0
for start in xrange(10):
temp = 0
for i in prime_lst[start:]:
temp += i
if temp > max_value:
break
if temp in prime_lst:
if i - start > len_res:
len_res = i - start
res = temp
return res
def solution1(value=CONST):
"""
Bryukh's solution
Try without primedivisors
>>> solution(2)
14
>>> solution(3)
644
"""
pr_list = eratosthenes(100000)
x = 10
while True:
x_divisors = [0] * value
for i in range(value):
for pr in pr_list:
if not (x+i) % pr:
x_divisors[i] += 1
if pr > (x+i)/2:
break
if all([xd==value for xd in x_divisors]):
break
x += 1
return x
def solution():
"""
Bryukh's solution
>>> solution()
26033
"""
prlist = eratosthenes(10000)
for p1 in prlist[:-4]:
for p2 in prlist[prlist.index(p1)+1:-3]:
if not_conc_prime(p1, p2):
continue
for p3 in prlist[prlist.index(p2)+1:-2]:
if not_conc_prime(p1, p3) or not_conc_prime(p2, p3):
continue
for p4 in prlist[prlist.index(p3)+1:-1]:
if (not_conc_prime(p1, p4) or not_conc_prime(p2, p4) or
not_conc_prime(p3, p4)):
continue
for p5 in prlist[prlist.index(p4)+1:]:
if (not_conc_prime(p1, p5) or not_conc_prime(p2, p5) or
not_conc_prime(p3, p5) or not_conc_prime(p4, p5)):
continue
return sum((p1, p2, p3, p4, p5))
def solution():
"""
Bryukh's solution
>>> solution()
26033
"""
prlist = eratosthenes(10000)
for p1 in prlist[:-4]:
for p2 in prlist[prlist.index(p1) + 1:-3]:
if not_conc_prime(p1, p2):
continue
for p3 in prlist[prlist.index(p2) + 1:-2]:
if not_conc_prime(p1, p3) or not_conc_prime(p2, p3):
continue
for p4 in prlist[prlist.index(p3) + 1:-1]:
if (not_conc_prime(p1, p4) or not_conc_prime(p2, p4)
or not_conc_prime(p3, p4)):
continue
for p5 in prlist[prlist.index(p4) + 1:]:
if (not_conc_prime(p1, p5) or not_conc_prime(p2, p5)
or not_conc_prime(p3, p5)
or not_conc_prime(p4, p5)):
continue
return sum((p1, p2, p3, p4, p5))
def solution():
"""
Bryukh's solution
>>> solution()
[148748178147, 296962999629]
"""
res = []
pr_list = eratosthenes(10000)
pr_list = pr_list[pr_list.index(1009):]
while pr_list:
pr = pr_list[0]
pr_per = [int(''.join(var)) for var in permutations(str(pr))
if int(''.join(var)) in pr_list]
pr_per = sorted(list(set(pr_per)))
for x in pr_per:
pr_list.remove(x)
if len(set(pr_per)) < 3:
continue
for i in xrange(len(pr_per)-2):
for j in xrange(i+1, len(pr_per)-1):
third = pr_per[j] + (pr_per[j] - pr_per[i])
if third in pr_per:
res.append(pr_per[i]*(10**8) + pr_per[j]*(10**4) + third)
return res
