9743 = (2 * 4871) + 1 ;
hence not 2 divides 9743 by NAT_4:9; :: thesis:
9743 = (3 * 3247) + 2 ;
hence not 3 divides 9743 by NAT_4:9; :: thesis:
9743 = (5 * 1948) + 3 ;
hence not 5 divides 9743 by NAT_4:9; :: thesis:
9743 = (7 * 1391) + 6 ;
hence not 7 divides 9743 by NAT_4:9; :: thesis:
9743 = (11 * 885) + 8 ;
hence not 11 divides 9743 by NAT_4:9; :: thesis:
9743 = (13 * 749) + 6 ;
hence not 13 divides 9743 by NAT_4:9; :: thesis:
9743 = (17 * 573) + 2 ;
hence not 17 divides 9743 by NAT_4:9; :: thesis:
9743 = (19 * 512) + 15 ;
hence not 19 divides 9743 by NAT_4:9; :: thesis:
9743 = (23 * 423) + 14 ;
hence not 23 divides 9743 by NAT_4:9; :: thesis:
9743 = (29 * 335) + 28 ;
hence not 29 divides 9743 by NAT_4:9; :: thesis:
9743 = (31 * 314) + 9 ;
hence not 31 divides 9743 by NAT_4:9; :: thesis:
9743 = (37 * 263) + 12 ;
hence not 37 divides 9743 by NAT_4:9; :: thesis:
9743 = (41 * 237) + 26 ;
hence not 41 divides 9743 by NAT_4:9; :: thesis:
9743 = (43 * 226) + 25 ;
hence not 43 divides 9743 by NAT_4:9; :: thesis:
9743 = (47 * 207) + 14 ;
hence not 47 divides 9743 by NAT_4:9; :: thesis:
9743 = (53 * 183) + 44 ;
hence not 53 divides 9743 by NAT_4:9; :: thesis:
9743 = (59 * 165) + 8 ;
hence not 59 divides 9743 by NAT_4:9; :: thesis:
9743 = (61 * 159) + 44 ;
hence not 61 divides 9743 by NAT_4:9; :: thesis:
9743 = (67 * 145) + 28 ;
hence not 67 divides 9743 by NAT_4:9; :: thesis:
9743 = (71 * 137) + 16 ;
hence not 71 divides 9743 by NAT_4:9; :: thesis:
9743 = (73 * 133) + 34 ;
hence not 73 divides 9743 by NAT_4:9; :: thesis:
9743 = (79 * 123) + 26 ;
hence not 79 divides 9743 by NAT_4:9; :: thesis:
9743 = (83 * 117) + 32 ;
hence not 83 divides 9743 by NAT_4:9; :: thesis:
9743 = (89 * 109) + 42 ;
hence not 89 divides 9743 by NAT_4:9; :: thesis:
9743 = (97 * 100) + 43 ;
hence not 97 divides 9743 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9743 & n is prime holds
not n divides 9743 by XPRIMET1:50;
hence 9743 is prime by NAT_4:14; :: thesis: