4283 = (2 * 2141) + 1 ;
hence not 2 divides 4283 by NAT_4:9; :: thesis:
4283 = (3 * 1427) + 2 ;
hence not 3 divides 4283 by NAT_4:9; :: thesis:
4283 = (5 * 856) + 3 ;
hence not 5 divides 4283 by NAT_4:9; :: thesis:
4283 = (7 * 611) + 6 ;
hence not 7 divides 4283 by NAT_4:9; :: thesis:
4283 = (11 * 389) + 4 ;
hence not 11 divides 4283 by NAT_4:9; :: thesis:
4283 = (13 * 329) + 6 ;
hence not 13 divides 4283 by NAT_4:9; :: thesis:
4283 = (17 * 251) + 16 ;
hence not 17 divides 4283 by NAT_4:9; :: thesis:
4283 = (19 * 225) + 8 ;
hence not 19 divides 4283 by NAT_4:9; :: thesis:
4283 = (23 * 186) + 5 ;
hence not 23 divides 4283 by NAT_4:9; :: thesis:
4283 = (29 * 147) + 20 ;
hence not 29 divides 4283 by NAT_4:9; :: thesis:
4283 = (31 * 138) + 5 ;
hence not 31 divides 4283 by NAT_4:9; :: thesis:
4283 = (37 * 115) + 28 ;
hence not 37 divides 4283 by NAT_4:9; :: thesis:
4283 = (41 * 104) + 19 ;
hence not 41 divides 4283 by NAT_4:9; :: thesis:
4283 = (43 * 99) + 26 ;
hence not 43 divides 4283 by NAT_4:9; :: thesis:
4283 = (47 * 91) + 6 ;
hence not 47 divides 4283 by NAT_4:9; :: thesis:
4283 = (53 * 80) + 43 ;
hence not 53 divides 4283 by NAT_4:9; :: thesis:
4283 = (59 * 72) + 35 ;
hence not 59 divides 4283 by NAT_4:9; :: thesis:
4283 = (61 * 70) + 13 ;
hence not 61 divides 4283 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 4283 & n is prime holds
not n divides 4283 by XPRIMET1:36;
hence 4283 is prime by NAT_4:14; :: thesis: