def do():
for a in range(len(nnz)):
for b in range(len(num)):
for c in range(len(num)):
for d in range(len(num)):
s = str(nnz[a]) + str(num[b]) + str(num[c]) + str(num[d])
if len(lex(s)) > 2:
for i in range(len(lex(s))):
for k in range(i + 2, len(lex(s))):
for j in range(i + 1, k):
if is_prime(lex(s)[i]) and is_prime(
lex(s)[j]) and is_prime(
lex(s)[k]) and lex(s)[i] + lex(
s)[k] == 2 * lex(s)[j]:
print(lex(s)[i], lex(s)[j], lex(s)[k])
if 1487 not in [
lex(s)[i],
lex(s)[j],
lex(s)[k]
]:
print("Answer: " + "".join([
str(lex(s)[i]),
str(lex(s)[j]),
str(lex(s)[k])
]))
return
print(s) # track
def pandipri(n):
panpri = []
num = [] # all 1-digit numbers from 1 to n
int_num = []
for i in range(n):
num.append(str(i + 1))
int_num.append(i + 1)
perm = list(itertools.permutations(int_num))
perm_list = []
for i in range(len(perm)):
joined = ''
for j in range(n):
joined += str(perm[i][j])
perm_list.append(int(joined))
for count in range(len(perm_list)): # DUMMY COMMAND
pan = 0
for i in range(len(num)):
if num[i] in list(str(perm_list[count])):
pan += 1
if pan == n and is_prime(perm_list[count]):
panpri.append(perm_list[count])
if panpri:
print(f"{n} digits: {panpri[-1]}")
else:
print(f"{n} digits: No solution")
def hpf(n):
result = 1 # some small number
for i in range(n):
if n % (i + 1) == 0 and is_prime(i + 1):
result = i + 1
print(result) # track
return result
from check_primes import is_prime
num = 11
count = 0
answer = 0
while count < 11:
flag = True
n1 = num
n2 = num
# truncatable from right to left
for _ in range(len(str(num))):
if is_prime(n1):
n1 //= 10
else:
flag = False
break
# truncatable from left to right
if flag:
for i in range(len(str(num))):
if is_prime(n2):
n2 %= 10**(len(str(num))-i-1)
else:
flag = False
break
if flag:
answer += num
count += 1
print(num)
from check_primes import is_prime
n = 1
answer = 2 # counted 2 as a prime number so we can skip it
while n < 2_000_000:
if is_prime(n):
answer += n
n += 2
print(answer)
from number_theory import gcd
from check_primes import is_prime
q = 10**6
totient = lambda x: len(list(filter(lambda y: gcd(x, y) == 1, range(1, x))))
"""
ans = 0
n_ans = 0
for n in range(2,q+1):
totient_value = totient(n)
if n/totient_value > ans:
ans = n/totient_value
n_ans = n
"""
# You can run the above if you want, might take a lot of time.
# But think about this, what if we want to minimize totient(n)?
# Then we must as many prime factors as possible!
# So it's simply 2 x 3 x 5 x 7 x ... until it's still less then 1 million.
p = 0
result = 1
while result <= q:
if is_prime(p):
if result * p <= q:
result *= p
else:
break
p += 1
print(result)
es = list(4 * (i + 1)**2 - 4 * (i + 1) + 1 for i in range(1, diag))
ws = list(4 * (i + 1)**2 - 6 * (i + 1) + 3 for i in range(1, diag))
nw = list(4 * (i + 1)**2 - 8 * (i + 1) + 5 for i in range(1, diag))
result = [1] + ne + es + ws + nw
return len(list(filter(is_prime, result))) / len(result) * 100
##i = 5
##while spiral2(i) >= 10:
## i += 2
## print(i)
##print('DONE',i)
prime = 8
numbers = 13
spiral = 7
while prime / numbers >= 0.1:
#print(spiral)
diag = (spiral + 1) // 2
if is_prime(4 * (diag + 1)**2 - 10 * (diag + 1) + 7):
prime += 1
if is_prime(4 * (diag + 1)**2 - 8 * (diag + 1) + 5):
prime += 1
if is_prime(4 * (diag + 1)**2 - 6 * (diag + 1) + 3):
prime += 1
if is_prime(4 * (diag + 1)**2 - 4 * (diag + 1) + 1):
prime += 1
numbers += 4
spiral += 2
print('DONE', spiral)
def concat_prime(n1,n2):
concat1 = n1*10**(math.floor(math.log10(n2))+1)+n2
concat2 = n2*10**(math.floor(math.log10(n1))+1)+n1
return is_prime(concat1) and is_prime(concat2)
from check_primes import is_prime
answer = 1 # 2 is already included
passer = [0,2,4,5,6,8]
for count in range(3,10**6):
if count < 10 and is_prime(count):
answer += 1
continue
digits = list(map(int,str(count)))
if False in list(filter(lambda x: x in passer, digits)):
continue
flag = True
n = count
for _ in range(len(digits)):
if is_prime(n):
n = (n//10)+(n%10)*(10**(len(digits)-1))
else:
flag = False
break
if flag:
answer += 1
print(answer)