Thompson PSL(2,q), q<=10000: 626 groups (2^r: [4, 8, 32, 128, 2048, 8192]; 3^r: [27, 243, 2187]; primes: 617, from 7 to 9973)
small (q<=49): [4, 7, 8, 13, 17, 23, 27, 32, 37, 43, 47]
random sample (40, seed 15751022): [73, 277, 283, 547, 607, 643, 733, 857, 877, 977, 1087, 1373, 1433, 1453, 1567, 2137, 2203, 2243, 2467, 2957, 3163, 3217, 4073, 4157, 4733, 4933, 5827, 6317, 6607, 6673, 7127, 7867, 7907, 7937, 8192, 8287, 8423, 8713, 8753, 9767]
forced extras: [128, 243, 2048, 2187, 9677, 9973]
next Thompson prime after 10^4: 10007
