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from bisect import bisect_left print('Generating 99,999 prime numbers... (Takes about 10 seconds)\n') #----------------------------------------------------------------------- def prime_list(n): sieve = [True] * n for i in xrange(3, int(n ** 0.5) + 1, 2): if sieve[i]: sieve[i * i::2 * i]=[False]*((n - i * i - 1) / (2 * i) + 1) return [2] + [i for i in xrange(3, n, 2) if sieve[i]] biggest_prime = 1299721 # The 100,001st prime second_to_biggest_prime = 1299709 list_of_primes = prime_list(biggest_prime) def take_closest(the_list, num): pos = bisect_left(the_list, num) if pos == 0: return the_list[0] if pos == len(the_list): return the_list[-1] before = the_list[pos - 1] after = the_list[pos] if after - num < num - before: return after else: return before def prime_info(num): if num == 1: return 0, 2, 'None', 2 # 2 is the first prime, No previous prime, next prime is 2 if num == 2: return 1, 3, 'None', 3 number_of_prime = 0 nth_prime_number = 0 previous_prime = 0 next_prime = 0 if num > 99999: nth_prime_number = 'Unavailable' else: nth_prime_number = list_of_primes[num - 1] if num < second_to_biggest_prime: # The last prime before the biggest_prime if num in list_of_primes: number_of_prime = list_of_primes.index(num) + 1 previous_prime = list_of_primes[number_of_prime - 2] next_prime = list_of_primes[number_of_prime] else: prime = take_closest(list_of_primes, num) if num > prime: previous_prime = prime index = list_of_primes.index(previous_prime) + 1 next_prime = list_of_primes[index] else: next_prime = prime # Because the prime is greater than num index = list_of_primes.index(next_prime) - 1 previous_prime = list_of_primes[index] else: previous_prime = 'Unavailable' next_prime = 'Unavailable' return number_of_prime, nth_prime_number, previous_prime, next_prime #----------------------------------------------------------------------- for i in range(1, 1000): prime_num, nth_prime, previous_prime, next_prime = prime_info(i) print('\n\nNumber: ' + str(i)) print('Prime #' + str(i) + ' is ' + str(nth_prime)) the_nth_prime = nth_prime two_sum = i + nth_prime print('The sum of these two numbers is ' + str(two_sum)) prime_num, nth_prime, previous_prime, next_prime = prime_info(two_sum) if str(nth_prime) == 'Unavailable': exit() print('Prime #' + str(two_sum) + ' is ' + str(nth_prime)) answer = nth_prime if len(str(answer)) > len(str(two_sum)): shortened = str(answer)[:len(str(two_sum))] if shortened == str(the_nth_prime): raw_input(' Yes! ' + str(i) + ' self resolves!') # The results for this program are 261, 262, and 263
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