6151 = (2 * 3075) + 1 ;
hence not 2 divides 6151 by NAT_4:9; :: thesis:
6151 = (3 * 2050) + 1 ;
hence not 3 divides 6151 by NAT_4:9; :: thesis:
6151 = (5 * 1230) + 1 ;
hence not 5 divides 6151 by NAT_4:9; :: thesis:
6151 = (7 * 878) + 5 ;
hence not 7 divides 6151 by NAT_4:9; :: thesis:
6151 = (11 * 559) + 2 ;
hence not 11 divides 6151 by NAT_4:9; :: thesis:
6151 = (13 * 473) + 2 ;
hence not 13 divides 6151 by NAT_4:9; :: thesis:
6151 = (17 * 361) + 14 ;
hence not 17 divides 6151 by NAT_4:9; :: thesis:
6151 = (19 * 323) + 14 ;
hence not 19 divides 6151 by NAT_4:9; :: thesis:
6151 = (23 * 267) + 10 ;
hence not 23 divides 6151 by NAT_4:9; :: thesis:
6151 = (29 * 212) + 3 ;
hence not 29 divides 6151 by NAT_4:9; :: thesis:
6151 = (31 * 198) + 13 ;
hence not 31 divides 6151 by NAT_4:9; :: thesis:
6151 = (37 * 166) + 9 ;
hence not 37 divides 6151 by NAT_4:9; :: thesis:
6151 = (41 * 150) + 1 ;
hence not 41 divides 6151 by NAT_4:9; :: thesis:
6151 = (43 * 143) + 2 ;
hence not 43 divides 6151 by NAT_4:9; :: thesis:
6151 = (47 * 130) + 41 ;
hence not 47 divides 6151 by NAT_4:9; :: thesis:
6151 = (53 * 116) + 3 ;
hence not 53 divides 6151 by NAT_4:9; :: thesis:
6151 = (59 * 104) + 15 ;
hence not 59 divides 6151 by NAT_4:9; :: thesis:
6151 = (61 * 100) + 51 ;
hence not 61 divides 6151 by NAT_4:9; :: thesis:
6151 = (67 * 91) + 54 ;
hence not 67 divides 6151 by NAT_4:9; :: thesis:
6151 = (71 * 86) + 45 ;
hence not 71 divides 6151 by NAT_4:9; :: thesis:
6151 = (73 * 84) + 19 ;
hence not 73 divides 6151 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 6151 & n is prime holds
not n divides 6151 by XPRIMET1:42;
hence 6151 is prime by NAT_4:14; :: thesis: