PASS A1 subgroup of A_5 x SL_2(4) generated by (a,A), (b,B) is the graph of an isomorphism: order 60, 60 even permutations, 60 matrices of determinant 1
PASS A2 elements of orders 5 and 3 have no nonzero fixed vector on F_4^2: {(1, 1, 1, 1, 1): [15], (2, 2, 1): [3], (3, 1, 1): [0], (5,): [0]}
PASS A3 no line of F_4^2 is invariant (irreducible over F_4)
PASS B1 certificate r = 2: sum of coef * (sum of z k, k in K) = identity in F_2A_7: 1251 terms, cycle types of the generators {(5, 1, 1): 726, (7,): 525}, 240 distinct subgroups K
PASS B1c negative control r = 2: dropping the first term destroys the identity
PASS B2 certificate r = 3: sum of coef * (sum of z k, k in K) = identity in F_3A_7: 1675 terms, cycle types of the generators {(7,): 706, (5, 1, 1): 969}, 245 distinct subgroups K
PASS B2c negative control r = 3: dropping the first term destroys the identity
PASS C1 A_7-classes: the 5-cycles form one class (504); the 7-cycles split, g^2 ~ g, g^3 not ~ g
PASS C2 conjugates of P and H in A_7 and their left cosets: 120 + 126 = 246 subgroups, 106704 cosets
PASS D1 lcm(p-1,p-3) = (p-1)(p-3)/2; lcm(p-3,(p-1)/2) > p (p >= 7); (p-1)(p-3)/2 > 2(p-1) (p > 7): twin primes p <= 200: [5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199]
PASS D2 Zolotarev: the sign of x -> jx on Z/p is the Legendre symbol (j/p)
PASS D3 p = 5: dim 4, phi(g) = -1, phi(h) = -2 satisfy the criterion of Lemma 2.4(i)
PASS E1 chi^lambda(p-cycle) = (-1)^leg for hooks, 0 otherwise (p = 5, 7, 13, 19, all partitions)
PASS E2 hook degrees C(p-1,k); p = 5: the hooks of degree 4 are (4,1), (2,1,1,1), value +1 at a 3-cycle
PASS F1 abacus r-core = r-core by rim-hook removal (all partitions of 13, r = 2, 3, 5, 7)
PASS F2 r-blocks of S_p with p/2 < r < p-2 contain at most two hooks; hook cores have size p-r >= 2: 124 pairs (p, r) with p <= 200 a twin prime; largest number of hooks in a block: 2; all partitions checked for p = 13, 19
PASS F2c control: for r < p/2 the bound fails (p = 13, r = 3: a 3-block of S_13 with more than two hooks): largest number of hooks in a 3-block: 5
PASS G1 (q-3)(q-5) - (q-1)(q-7) = 8 and (q-5)(q-7) - (q-3)(q-9) = 8 as polynomials
PASS G2 Lemma 4.1 for q = 11, 17: y*t ~ z in S_p for every cycle type with >= 2 fixed points; the four elements; determinants 8
TOTAL failures: 0 
