6203 = (2 * 3101) + 1 ;
hence not 2 divides 6203 by NAT_4:9; :: thesis:
6203 = (3 * 2067) + 2 ;
hence not 3 divides 6203 by NAT_4:9; :: thesis:
6203 = (5 * 1240) + 3 ;
hence not 5 divides 6203 by NAT_4:9; :: thesis:
6203 = (7 * 886) + 1 ;
hence not 7 divides 6203 by NAT_4:9; :: thesis:
6203 = (11 * 563) + 10 ;
hence not 11 divides 6203 by NAT_4:9; :: thesis:
6203 = (13 * 477) + 2 ;
hence not 13 divides 6203 by NAT_4:9; :: thesis:
6203 = (17 * 364) + 15 ;
hence not 17 divides 6203 by NAT_4:9; :: thesis:
6203 = (19 * 326) + 9 ;
hence not 19 divides 6203 by NAT_4:9; :: thesis:
6203 = (23 * 269) + 16 ;
hence not 23 divides 6203 by NAT_4:9; :: thesis:
6203 = (29 * 213) + 26 ;
hence not 29 divides 6203 by NAT_4:9; :: thesis:
6203 = (31 * 200) + 3 ;
hence not 31 divides 6203 by NAT_4:9; :: thesis:
6203 = (37 * 167) + 24 ;
hence not 37 divides 6203 by NAT_4:9; :: thesis:
6203 = (41 * 151) + 12 ;
hence not 41 divides 6203 by NAT_4:9; :: thesis:
6203 = (43 * 144) + 11 ;
hence not 43 divides 6203 by NAT_4:9; :: thesis:
6203 = (47 * 131) + 46 ;
hence not 47 divides 6203 by NAT_4:9; :: thesis:
6203 = (53 * 117) + 2 ;
hence not 53 divides 6203 by NAT_4:9; :: thesis:
6203 = (59 * 105) + 8 ;
hence not 59 divides 6203 by NAT_4:9; :: thesis:
6203 = (61 * 101) + 42 ;
hence not 61 divides 6203 by NAT_4:9; :: thesis:
6203 = (67 * 92) + 39 ;
hence not 67 divides 6203 by NAT_4:9; :: thesis:
6203 = (71 * 87) + 26 ;
hence not 71 divides 6203 by NAT_4:9; :: thesis:
6203 = (73 * 84) + 71 ;
hence not 73 divides 6203 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 6203 & n is prime holds
not n divides 6203 by XPRIMET1:42;
hence 6203 is prime by NAT_4:14; :: thesis: