|PSL(2,10007)| = 501050730168 (expect 501050730168)
10001 = 73*137 ; 10003 = 7*1429 ; 10007 prime: True ; 10007 mod 5, 16, 7 = 2 7 4
|PSL(2,2^17)| = 2.2518e+15  > |PSL(2,10007)|: True
|PSL(2,3^11)| = 2.7795e+15  > |PSL(2,10007)|: True
|Sz(2^11)| = 3.6011e+16  > |PSL(2,10007)|: True
|PSL(2,2^13)| = 5.4976e+11  > |PSL(2,10007)|: True
minimal simple groups of order < |PSL(2,10007)|: 629 (non-PSL(2,p): ['PSL(2,2^2)', 'PSL(2,2^3)', 'PSL(2,3^3)', 'Sz(2^3)', 'PSL(2,2^5)', 'PSL(2,3^5)', 'Sz(2^5)', 'PSL(2,2^7)', 'PSL(2,3^7)', 'Sz(2^7)', 'PSL(2,2^11)', 'PSL(3,3)']); primes p: 617
all of them covered by Theorem 4.1: True
residues mod 560 coprime with r = +-2 mod 5: 96; covered K: 48 (48/96), O: 24
P below 130 covered by the families (K): [7, 13, 17, 43, 47, 83, 97, 113, 127]  others: [23, 37, 53, 67, 73, 103, 107]
u_1 = +-u_2 != +-1, kappa != 2, number of trace triples (K): {5: 0, 7: 4, 11: 0, 13: 0, 17: 0, 19: 0, 23: 0, 29: 0, 31: 0, 37: 4, 41: 0, 43: 4}
  (recorded sweep, primes 17..83: solutions only at 37, 43, 67, 71, 79; here p <= 43 for comparison)
TOTAL failures: 0
