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类梅森素数

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已知F=2^n-n,当n为素数,F碰巧也是素数时,不防把F称作类梅森素数,想知道有哪些n满足F为类梅森素数?


IP属地:江苏来自Android客户端1楼2024-05-06 19:22回复
    n=2、3、13、19还有吗


    IP属地:江苏来自Android客户端2楼2024-05-06 19:24
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      运行这个 Python程序
      def is_prime(num):
      if num <= 1:
      return False
      if num <= 3:
      return True
      if num % 2 == 0 or num % 3 == 0:
      return False
      i = 5
      while i * i <= num:
      if num % i == 0 or num % (i + 2) == 0:
      return False
      i += 6
      return True
      def mersenne_prime(n):
      return 2**n - 1
      def find_mersenne_primes(prime_list):
      mersenne_primes = []
      for prime in prime_list:
      f_value = mersenne_prime(prime)
      if is_prime(f_value):
      mersenne_primes.append(prime)
      return mersenne_primes
      prime_list = [23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]
      mersenne_primes = find_mersenne_primes(prime_list)
      print("满足 F 也是素数的素数 n 为:")
      print(mersenne_primes)


      IP属地:广东3楼2024-05-07 11:11
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        很厉害


        IP属地:安徽来自iPhone客户端6楼2024-05-08 13:09
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          @基灵公爵


          IP属地:浙江7楼2024-05-09 00:17
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            楼主的猜想有意义,值得研究!


            IP属地:山西8楼2024-05-13 07:45
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              n=481801


              IP属地:浙江9楼2024-06-19 15:55
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