== A_7: exact Engel depth and minimal law
   |A_7| = 2520, classes 9, mu(A_7) = 15, minimal law s = 35295   [0.0s]
   Lemma 2.4(b): (n, least k with [rho,_k tau] = 1) = [(2, 2), (3, 3), (4, 4), (5, 5), (6, 6)]
== Corollary 5.4 arithmetic
   15015 = 15015; odd n < 200 not decided for r = 61: [17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61]...; equal to the n with gcd(n,15015) = 1: True; smallest 17; min B_d = 62
   r = 3: undecided odd n < 60: [17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59]
   r = 61: undecided odd n < 60: [17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59]
   r = 62: undecided odd n < 60: [3, 17, 19, 23, 29, 31, 37, 41, 43, 47, 51, 53, 57, 59]
== Section 5.2 on random pairs, Sz(32) and Sz(128): y = M(c), x random (U(a,b)M(k)TU(a',b'))
   q = 32: 300 random pairs; with some a_j exchanging <e_1>, <e_4>: 135; tail = j+2 in 135; more than one such j: 0   [6.5s]
   q = 128: 40 random pairs; with some a_j exchanging <e_1>, <e_4>: 12; tail = j+2 in 12; more than one such j: 0   [72.7s]
== Remark 3.6(1)
   least odd primes p with a point with s != 0 and c != 0, r = 1..7: [7, 7, 11, 11, 13, 19, 19]
   same with s = 0 allowed: [3, 7, 11, 11, 13, 19, 19]; (h,s) = (3,0) lies on C over F_5 for r = 1: True
   primes 1000 < p < 3000: 262; pairs (p, r <= 4) without a point with s != 0, c != 0: []
   r = 3: odd prime powers q <= 30000: 3306; those without an F_q-point with c != 0: [3, 5, 7, 9]   [4.7s]
exit=0
