def main():
upper = 100000
max_consecutives = 0
max_consecutives_prime = 0
count = 1
sum_primes = [2]
for i in range(3, upper, 2):
if is_prime(i):
count += 1
for index in range(0, len(sum_primes) - max_consecutives):
sum_primes[index] += i
temp = sum_primes[index]
if temp > upper:
continue
if is_prime(temp) and max_consecutives < count - index:
max_consecutives = count - index
max_consecutives_prime = temp
sum_primes.append(i)
print("{}-{}".format(max_consecutives_prime, max_consecutives))
return 0
def count_spiral_primes(k):
count = 0
bottom_right = k*k
bottom_left = bottom_right - k + 1
top_left = bottom_left - k + 1
top_right = top_left - k + 1
return is_prime(bottom_left) + is_prime(top_left) + is_prime(top_right)
def prime_pairs(primes):
pairs = findsubsets(primes, 2)
for pair in pairs:
pair0 = concatenating(pair[0], pair[1])
pair1 = concatenating(pair[1], pair[0])
if not is_prime(pair0) or not is_prime(pair1):
return False
return True
def main():
index = 11
primes = [{3}, {5}, {7}]
set_primes = 5
while True:
if is_prime(index):
if {index} not in primes:
for e in primes:
if prime_pair_number_with_list(index, e):
temp = {index} | e
if len(temp) == set_primes:
print(temp)
sum60 = 0
for e in temp:
sum += e
print(sum60)
return 0
primes.append(temp)
primes.append({index})
index += 2
return 0
def main():
blacklist = set()
for i in range(1001, 9999, 2):
if is_prime(i):
temp = number_permutations(i)
p_i = sorted([i for i in temp if is_prime(i) and len(str(i)) == 4])
if i not in blacklist:
if len(p_i) >= 3:
for e in findsubsets(p_i,3):
if is_arithmetic(e):
print(''.join(str(j) for j in e))
blacklist |= {i for i in p_i}
return 0
def get_prime(n):
index = 1
count = 1 # already count 2 as prime
if n < 1:
return None
if n == 1:
return 2
while count < n:
index += 2
if is_prime(index):
count += 1
return index
def main():
upper = 2000000
sum10 = 2
index = 3
while index < upper:
if is_prime(index):
sum10 += index
index += 2
print(sum10)
return 0
def main():
index = 11
start_sequence = 0 #store the first of sequences, also result
num = 8
while True:
slices = [i for i in range(0, len(str(index)) - 1)]
for j in range(1, len(str(index))):
mask = findsubsets(slices,
j) # get all the ways to replace digits with *
for e in mask:
temp = str(index)
count = 0
sequences = []
for i in range(0, 10):
for k in e:
temp = temp[:k] + str(i) + temp[k + 1:]
if temp[0] == '0':
continue # ignore when replace first digit with 0
if (is_prime(int(temp))):
count += 1
sequences.append(temp)
if count == num:
print("Found: {}, e={}".format(str(index), e))
print(sequences)
print(sequences[0])
return 0
index += 2
return 0
def main():
index = 9
primes = {2, 3, 5, 7}
while True:
if is_prime(index):
primes |= {index}
else:
count = len(primes)
for e in primes:
if (index - e)%2 == 0 and is_square_number((index-e)/2):
print("{}={} + 2x{}^2".format(index, e, int(math.sqrt((index -e)/2))))
break
else:
count -= 1
if count == 0:
print("Found: {}".format(index))
break
index += 2
return 0
def prime_factors(p):
factors = {}
index = 2
temp = p
while index < p:
if mymodule.is_prime(temp):
factors[temp] = 1
break
if temp % index == 0:
if index in factors:
factors[index] += 1
else:
factors[index] = 1
temp = int(temp / index)
continue
index += 1
return factors
def prime_pair(p, q):
pair0 = concatenating(p, q)
pair1 = concatenating(q, p)
return is_prime(pair0) and is_prime(pair1)
import mymodule
print("73 is Prime:", mymodule.is_prime(73))
print("73 Number of Factors:", mymodule.num_factors(73))
