{
  "degree": 2,
  "B": "20+3*(L+1)",
  "condition": "p>B^200000; L=ceil(log2(p))",
  "first_upper_endpoint_crossing": 4753080,
  "previous_L": 4753079,
  "exact_adjacent_checks": true,
  "lower_B_power_bit_length": 4753080,
  "upper_B_power_bit_length": 4753080,
  "monotonicity_argument": "g(L)=L ln2-200000 ln(23+3L) has increasing derivative and becomes increasing after L>200000/ln2-23/3; g(1)<0, and g(1000000)<0. Exact adjacent checks certify the first integer crossing.",
  "interpretation": "Necessary boundary only: no prime at the crossing was constructed, and larger n increases B. The bound is not a measured runtime or a lower bound on algorithm cost.",
  "source_exponents": {
    "small_prime_guard": 200000,
    "auxiliary_prime_bound": 20000000,
    "total_B_exponent": 500000,
    "total_E_exponent": 20,
    "substituted_B_exponent": 400000100,
    "headline": 1000000000000
  },
  "auxiliary_prime_note": "Runtime is polynomial in numeric E, not log E; hidden absolute constant c0 is not selected."
}