primes scanned: 348511 (5 <= p <= 5000000)
k(PSL(2,27)) by the general Dickson list: 12, O = [1, 2, 3, 4, 7, 9, 12, 13, 14, 26, 27, 28, 351, 9828]
values k <= 400 not attained by a prime p <= X: [8, 12, 324, 332, 346, 348, 359, 360, 364, 367, 370, 371, 372, 375, 376, 377, 378, 380, 384, 386, 387, 388, 392, 393, 394, 396, 398, 399]
every k in {7} u [9,323] minus {12} is attained by a prime; 12 by q = 27: True
largest least prime among k in {7} u [9,323] minus {12}: (4022201, 268)
least p for k = 7, 9, 10, 11, 13, 14, 323: [(7, 5), (9, 7), (10, 11), (11, 13), (13, 47), (14, 17), (323, 3243239)]
least p for k = 268: 4022201; for k = 324: None
