6113 = (2 * 3056) + 1 ;
hence not 2 divides 6113 by NAT_4:9; :: thesis:
6113 = (3 * 2037) + 2 ;
hence not 3 divides 6113 by NAT_4:9; :: thesis:
6113 = (5 * 1222) + 3 ;
hence not 5 divides 6113 by NAT_4:9; :: thesis:
6113 = (7 * 873) + 2 ;
hence not 7 divides 6113 by NAT_4:9; :: thesis:
6113 = (11 * 555) + 8 ;
hence not 11 divides 6113 by NAT_4:9; :: thesis:
6113 = (13 * 470) + 3 ;
hence not 13 divides 6113 by NAT_4:9; :: thesis:
6113 = (17 * 359) + 10 ;
hence not 17 divides 6113 by NAT_4:9; :: thesis:
6113 = (19 * 321) + 14 ;
hence not 19 divides 6113 by NAT_4:9; :: thesis:
6113 = (23 * 265) + 18 ;
hence not 23 divides 6113 by NAT_4:9; :: thesis:
6113 = (29 * 210) + 23 ;
hence not 29 divides 6113 by NAT_4:9; :: thesis:
6113 = (31 * 197) + 6 ;
hence not 31 divides 6113 by NAT_4:9; :: thesis:
6113 = (37 * 165) + 8 ;
hence not 37 divides 6113 by NAT_4:9; :: thesis:
6113 = (41 * 149) + 4 ;
hence not 41 divides 6113 by NAT_4:9; :: thesis:
6113 = (43 * 142) + 7 ;
hence not 43 divides 6113 by NAT_4:9; :: thesis:
6113 = (47 * 130) + 3 ;
hence not 47 divides 6113 by NAT_4:9; :: thesis:
6113 = (53 * 115) + 18 ;
hence not 53 divides 6113 by NAT_4:9; :: thesis:
6113 = (59 * 103) + 36 ;
hence not 59 divides 6113 by NAT_4:9; :: thesis:
6113 = (61 * 100) + 13 ;
hence not 61 divides 6113 by NAT_4:9; :: thesis:
6113 = (67 * 91) + 16 ;
hence not 67 divides 6113 by NAT_4:9; :: thesis:
6113 = (71 * 86) + 7 ;
hence not 71 divides 6113 by NAT_4:9; :: thesis:
6113 = (73 * 83) + 54 ;
hence not 73 divides 6113 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 6113 & n is prime holds
not n divides 6113 by XPRIMET1:42;
hence 6113 is prime by NAT_4:14; :: thesis: