4703 = (2 * 2351) + 1 ;
hence not 2 divides 4703 by NAT_4:9; :: thesis:
4703 = (3 * 1567) + 2 ;
hence not 3 divides 4703 by NAT_4:9; :: thesis:
4703 = (5 * 940) + 3 ;
hence not 5 divides 4703 by NAT_4:9; :: thesis:
4703 = (7 * 671) + 6 ;
hence not 7 divides 4703 by NAT_4:9; :: thesis:
4703 = (11 * 427) + 6 ;
hence not 11 divides 4703 by NAT_4:9; :: thesis:
4703 = (13 * 361) + 10 ;
hence not 13 divides 4703 by NAT_4:9; :: thesis:
4703 = (17 * 276) + 11 ;
hence not 17 divides 4703 by NAT_4:9; :: thesis:
4703 = (19 * 247) + 10 ;
hence not 19 divides 4703 by NAT_4:9; :: thesis:
4703 = (23 * 204) + 11 ;
hence not 23 divides 4703 by NAT_4:9; :: thesis:
4703 = (29 * 162) + 5 ;
hence not 29 divides 4703 by NAT_4:9; :: thesis:
4703 = (31 * 151) + 22 ;
hence not 31 divides 4703 by NAT_4:9; :: thesis:
4703 = (37 * 127) + 4 ;
hence not 37 divides 4703 by NAT_4:9; :: thesis:
4703 = (41 * 114) + 29 ;
hence not 41 divides 4703 by NAT_4:9; :: thesis:
4703 = (43 * 109) + 16 ;
hence not 43 divides 4703 by NAT_4:9; :: thesis:
4703 = (47 * 100) + 3 ;
hence not 47 divides 4703 by NAT_4:9; :: thesis:
4703 = (53 * 88) + 39 ;
hence not 53 divides 4703 by NAT_4:9; :: thesis:
4703 = (59 * 79) + 42 ;
hence not 59 divides 4703 by NAT_4:9; :: thesis:
4703 = (61 * 77) + 6 ;
hence not 61 divides 4703 by NAT_4:9; :: thesis:
4703 = (67 * 70) + 13 ;
hence not 67 divides 4703 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 4703 & n is prime holds
not n divides 4703 by XPRIMET1:38;
hence 4703 is prime by NAT_4:14; :: thesis: