L1 twin primes p <= 200: [5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199] (15)
L2 lcm, Zolotarev, inequalities for all 15 twin primes: True; lcm(p-3,(p-1)/2) for p = 7: 12, p = 13: 30, p = 31: 420; (p-1)(p-3)/2 for p = 31: 420
L3 (eq:mn) for all partitions of 5, 7, 13, 19: True; p = 5, degree-4 characters at a 3-cycle: {(4, 1): 1, (2, 1, 1, 1): 1} (fixed-point-freeness would need -2)
L4 Lemma 3.2 hook count for 124 pairs (p, r), p <= 200, p/2 < r < p-2: True; control (r < p/2 with a block of more than two hooks) holds for 189 pairs, e.g. [(5, 2), (7, 2), (7, 3), (13, 2)]
L5 constants 8 (polynomial identities), conjugacy y t ~ z for 206 cycle types (q = 11, 17), and pi >= 2 for the four elements iff q >= 8: True
TOTAL failures: 0
