6037 = (2 * 3018) + 1 ;
hence not 2 divides 6037 by NAT_4:9; :: thesis:
6037 = (3 * 2012) + 1 ;
hence not 3 divides 6037 by NAT_4:9; :: thesis:
6037 = (5 * 1207) + 2 ;
hence not 5 divides 6037 by NAT_4:9; :: thesis:
6037 = (7 * 862) + 3 ;
hence not 7 divides 6037 by NAT_4:9; :: thesis:
6037 = (11 * 548) + 9 ;
hence not 11 divides 6037 by NAT_4:9; :: thesis:
6037 = (13 * 464) + 5 ;
hence not 13 divides 6037 by NAT_4:9; :: thesis:
6037 = (17 * 355) + 2 ;
hence not 17 divides 6037 by NAT_4:9; :: thesis:
6037 = (19 * 317) + 14 ;
hence not 19 divides 6037 by NAT_4:9; :: thesis:
6037 = (23 * 262) + 11 ;
hence not 23 divides 6037 by NAT_4:9; :: thesis:
6037 = (29 * 208) + 5 ;
hence not 29 divides 6037 by NAT_4:9; :: thesis:
6037 = (31 * 194) + 23 ;
hence not 31 divides 6037 by NAT_4:9; :: thesis:
6037 = (37 * 163) + 6 ;
hence not 37 divides 6037 by NAT_4:9; :: thesis:
6037 = (41 * 147) + 10 ;
hence not 41 divides 6037 by NAT_4:9; :: thesis:
6037 = (43 * 140) + 17 ;
hence not 43 divides 6037 by NAT_4:9; :: thesis:
6037 = (47 * 128) + 21 ;
hence not 47 divides 6037 by NAT_4:9; :: thesis:
6037 = (53 * 113) + 48 ;
hence not 53 divides 6037 by NAT_4:9; :: thesis:
6037 = (59 * 102) + 19 ;
hence not 59 divides 6037 by NAT_4:9; :: thesis:
6037 = (61 * 98) + 59 ;
hence not 61 divides 6037 by NAT_4:9; :: thesis:
6037 = (67 * 90) + 7 ;
hence not 67 divides 6037 by NAT_4:9; :: thesis:
6037 = (71 * 85) + 2 ;
hence not 71 divides 6037 by NAT_4:9; :: thesis:
6037 = (73 * 82) + 51 ;
hence not 73 divides 6037 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 6037 & n is prime holds
not n divides 6037 by XPRIMET1:42;
hence 6037 is prime by NAT_4:14; :: thesis: