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))