4793 = (2 * 2396) + 1 ;
hence not 2 divides 4793 by NAT_4:9; :: thesis:
4793 = (3 * 1597) + 2 ;
hence not 3 divides 4793 by NAT_4:9; :: thesis:
4793 = (5 * 958) + 3 ;
hence not 5 divides 4793 by NAT_4:9; :: thesis:
4793 = (7 * 684) + 5 ;
hence not 7 divides 4793 by NAT_4:9; :: thesis:
4793 = (11 * 435) + 8 ;
hence not 11 divides 4793 by NAT_4:9; :: thesis:
4793 = (13 * 368) + 9 ;
hence not 13 divides 4793 by NAT_4:9; :: thesis:
4793 = (17 * 281) + 16 ;
hence not 17 divides 4793 by NAT_4:9; :: thesis:
4793 = (19 * 252) + 5 ;
hence not 19 divides 4793 by NAT_4:9; :: thesis:
4793 = (23 * 208) + 9 ;
hence not 23 divides 4793 by NAT_4:9; :: thesis:
4793 = (29 * 165) + 8 ;
hence not 29 divides 4793 by NAT_4:9; :: thesis:
4793 = (31 * 154) + 19 ;
hence not 31 divides 4793 by NAT_4:9; :: thesis:
4793 = (37 * 129) + 20 ;
hence not 37 divides 4793 by NAT_4:9; :: thesis:
4793 = (41 * 116) + 37 ;
hence not 41 divides 4793 by NAT_4:9; :: thesis:
4793 = (43 * 111) + 20 ;
hence not 43 divides 4793 by NAT_4:9; :: thesis:
4793 = (47 * 101) + 46 ;
hence not 47 divides 4793 by NAT_4:9; :: thesis:
4793 = (53 * 90) + 23 ;
hence not 53 divides 4793 by NAT_4:9; :: thesis:
4793 = (59 * 81) + 14 ;
hence not 59 divides 4793 by NAT_4:9; :: thesis:
4793 = (61 * 78) + 35 ;
hence not 61 divides 4793 by NAT_4:9; :: thesis:
4793 = (67 * 71) + 36 ;
hence not 67 divides 4793 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 4793 & n is prime holds
not n divides 4793 by XPRIMET1:38;
hence 4793 is prime by NAT_4:14; :: thesis: