Attached are the results for k=33333, with n up to 370k.
41 primes:-
Code:
3, 4, 6, 14, 15, 20, 43, 44, 55, 56, 75, 78, 83, 155, 163, 190, 236, 283, 296, 356, 423, 656, 839, 899, 1940, 2126, 3030, 4879, 5395, 5523, 9919, 19875, 22988, 34803, 115638, 183475, 222203, 233766, 253100, 315755, 359644