code: def _lucas_lehmer_primality_test(p):
      r"""Test if the Mersenne number `M_p = 2^p-1` is prime.
  
      Parameters
      ==========
  
      p : int
          ``p`` is an odd prime number
  
      Returns
      =======
  
      bool : If ``True``, then `M_p` is the Mersenne prime
  
      Examples
      ========
  
      >>> from sympy.ntheory.primetest import _lucas_lehmer_primality_test
      >>> _lucas_lehmer_primality_test(5) # 2**5 - 1 = 31 is prime
      True
      >>> _lucas_lehmer_primality_test(11) # 2**11 - 1 = 2047 is not prime
      False
  
      See Also
      ========
  
      is_mersenne_prime
  
      References
      ==========
  
      .. [1] https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test
  
      """
      v = 4
      m = 2**p - 1
      for _ in range(p - 2):
          v = pow(v, 2, m) - 2
      return v == 0
  
imports: from itertools import count
  from sympy.core.sympify import sympify
  from sympy.external.gmpy import gmpy, gcd, jacobi, is_square, bit_scan1, is_fermat_prp, is_euler_prp, is_selfridge_prp, is_strong_selfridge_prp, is_strong_bpsw_prp
  from sympy.external.ntheory import _lucas_sequence
  from sympy.utilities.misc import as_int, filldedent
label_desc: Use image node_id 12 for calling a global function with example usage: _lucas_lehmer_primality_test(p) and returns: unknown