9067 = (2 * 4533) + 1 ;
hence not 2 divides 9067 by NAT_4:9; :: thesis:
9067 = (3 * 3022) + 1 ;
hence not 3 divides 9067 by NAT_4:9; :: thesis:
9067 = (5 * 1813) + 2 ;
hence not 5 divides 9067 by NAT_4:9; :: thesis:
9067 = (7 * 1295) + 2 ;
hence not 7 divides 9067 by NAT_4:9; :: thesis:
9067 = (11 * 824) + 3 ;
hence not 11 divides 9067 by NAT_4:9; :: thesis:
9067 = (13 * 697) + 6 ;
hence not 13 divides 9067 by NAT_4:9; :: thesis:
9067 = (17 * 533) + 6 ;
hence not 17 divides 9067 by NAT_4:9; :: thesis:
9067 = (19 * 477) + 4 ;
hence not 19 divides 9067 by NAT_4:9; :: thesis:
9067 = (23 * 394) + 5 ;
hence not 23 divides 9067 by NAT_4:9; :: thesis:
9067 = (29 * 312) + 19 ;
hence not 29 divides 9067 by NAT_4:9; :: thesis:
9067 = (31 * 292) + 15 ;
hence not 31 divides 9067 by NAT_4:9; :: thesis:
9067 = (37 * 245) + 2 ;
hence not 37 divides 9067 by NAT_4:9; :: thesis:
9067 = (41 * 221) + 6 ;
hence not 41 divides 9067 by NAT_4:9; :: thesis:
9067 = (43 * 210) + 37 ;
hence not 43 divides 9067 by NAT_4:9; :: thesis:
9067 = (47 * 192) + 43 ;
hence not 47 divides 9067 by NAT_4:9; :: thesis:
9067 = (53 * 171) + 4 ;
hence not 53 divides 9067 by NAT_4:9; :: thesis:
9067 = (59 * 153) + 40 ;
hence not 59 divides 9067 by NAT_4:9; :: thesis:
9067 = (61 * 148) + 39 ;
hence not 61 divides 9067 by NAT_4:9; :: thesis:
9067 = (67 * 135) + 22 ;
hence not 67 divides 9067 by NAT_4:9; :: thesis:
9067 = (71 * 127) + 50 ;
hence not 71 divides 9067 by NAT_4:9; :: thesis:
9067 = (73 * 124) + 15 ;
hence not 73 divides 9067 by NAT_4:9; :: thesis:
9067 = (79 * 114) + 61 ;
hence not 79 divides 9067 by NAT_4:9; :: thesis:
9067 = (83 * 109) + 20 ;
hence not 83 divides 9067 by NAT_4:9; :: thesis:
9067 = (89 * 101) + 78 ;
hence not 89 divides 9067 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9067 & n is prime holds
not n divides 9067 by XPRIMET1:48;
hence 9067 is prime by NAT_4:14; :: thesis: