code: def test_prps():
      oddcomposites = [
          n for n in range(1, 10**5) if n % 2 and not isprime(n)
      ]
      # A checksum would be better.
      assert sum(oddcomposites) == 2045603465
      assert [n for n in oddcomposites if mr(n, [2])] == [
          2047,
          3277,
          4033,
          4681,
          8321,
          15841,
          29341,
          42799,
          49141,
          52633,
          65281,
          74665,
          80581,
          85489,
          88357,
          90751,
      ]
      assert [n for n in oddcomposites if mr(n, [3])] == [
          121,
          703,
          1891,
          3281,
          8401,
          8911,
          10585,
          12403,
          16531,
          18721,
          19345,
          23521,
          31621,
          44287,
          47197,
          55969,
          63139,
          74593,
          79003,
          82513,
          87913,
          88573,
          97567,
      ]
      assert [n for n in oddcomposites if mr(n, [325])] == [
          9,
          25,
          27,
          49,
          65,
          81,
          325,
          341,
          343,
          697,
          1141,
          2059,
          2149,
          3097,
          3537,
          4033,
          4681,
          4941,
          5833,
          6517,
          7987,
          8911,
          12403,
          12913,
          15043,
          16021,
          20017,
          22261,
          23221,
          24649,
          24929,
          31841,
          35371,
          38503,
          43213,
          44173,
          47197,
          50041,
          55909,
          56033,
          58969,
          59089,
          61337,
          65441,
          68823,
          72641,
          76793,
          78409,
          85879,
      ]
      assert not any(
          mr(n, [9345883071009581737]) for n in oddcomposites
      )
      assert [n for n in oddcomposites if is_lucas_prp(n)] == [
          323,
          377,
          1159,
          1829,
          3827,
          5459,
          5777,
          9071,
          9179,
          10877,
          11419,
          11663,
          13919,
          14839,
          16109,
          16211,
          18407,
          18971,
          19043,
          22499,
          23407,
          24569,
          25199,
          25877,
          26069,
          27323,
          32759,
          34943,
          35207,
          39059,
          39203,
          39689,
          40309,
          44099,
          46979,
          47879,
          50183,
          51983,
          53663,
          56279,
          58519,
          60377,
          63881,
          69509,
          72389,
          73919,
          75077,
          77219,
          79547,
          79799,
          82983,
          84419,
          86063,
          90287,
          94667,
          97019,
          97439,
      ]
      assert [n for n in oddcomposites if is_strong_lucas_prp(n)] == [
          5459,
          5777,
          10877,
          16109,
          18971,
          22499,
          24569,
          25199,
          40309,
          58519,
          75077,
          97439,
      ]
      assert [
          n for n in oddcomposites if is_extra_strong_lucas_prp(n)
      ] == [
          989,
          3239,
          5777,
          10877,
          27971,
          29681,
          30739,
          31631,
          39059,
          72389,
          73919,
          75077,
      ]
  
file_path: sympy/sympy/ntheory/tests/test_primetest.py
imports: from math import gcd
  from sympy.ntheory.generate import Sieve, sieve
  from sympy.ntheory.primetest import mr, _lucas_extrastrong_params, is_lucas_prp, is_square, is_strong_lucas_prp, is_extra_strong_lucas_prp, proth_test, isprime, is_euler_pseudoprime, is_gaussian_prime, is_fermat_pseudoprime, is_euler_jacobi_pseudoprime, MERSENNE_PRIME_EXPONENTS, _lucas_lehmer_primality_test, is_mersenne_prime
  from sympy.testing.pytest import slow, raises
  from sympy.core.numbers import I
label_desc: Use image node_id 6 for calling a global function with example usage: test_prps() without return types