9421 = (2 * 4710) + 1 ;
hence not 2 divides 9421 by NAT_4:9; :: thesis:
9421 = (3 * 3140) + 1 ;
hence not 3 divides 9421 by NAT_4:9; :: thesis:
9421 = (5 * 1884) + 1 ;
hence not 5 divides 9421 by NAT_4:9; :: thesis:
9421 = (7 * 1345) + 6 ;
hence not 7 divides 9421 by NAT_4:9; :: thesis:
9421 = (11 * 856) + 5 ;
hence not 11 divides 9421 by NAT_4:9; :: thesis:
9421 = (13 * 724) + 9 ;
hence not 13 divides 9421 by NAT_4:9; :: thesis:
9421 = (17 * 554) + 3 ;
hence not 17 divides 9421 by NAT_4:9; :: thesis:
9421 = (19 * 495) + 16 ;
hence not 19 divides 9421 by NAT_4:9; :: thesis:
9421 = (23 * 409) + 14 ;
hence not 23 divides 9421 by NAT_4:9; :: thesis:
9421 = (29 * 324) + 25 ;
hence not 29 divides 9421 by NAT_4:9; :: thesis:
9421 = (31 * 303) + 28 ;
hence not 31 divides 9421 by NAT_4:9; :: thesis:
9421 = (37 * 254) + 23 ;
hence not 37 divides 9421 by NAT_4:9; :: thesis:
9421 = (41 * 229) + 32 ;
hence not 41 divides 9421 by NAT_4:9; :: thesis:
9421 = (43 * 219) + 4 ;
hence not 43 divides 9421 by NAT_4:9; :: thesis:
9421 = (47 * 200) + 21 ;
hence not 47 divides 9421 by NAT_4:9; :: thesis:
9421 = (53 * 177) + 40 ;
hence not 53 divides 9421 by NAT_4:9; :: thesis:
9421 = (59 * 159) + 40 ;
hence not 59 divides 9421 by NAT_4:9; :: thesis:
9421 = (61 * 154) + 27 ;
hence not 61 divides 9421 by NAT_4:9; :: thesis:
9421 = (67 * 140) + 41 ;
hence not 67 divides 9421 by NAT_4:9; :: thesis:
9421 = (71 * 132) + 49 ;
hence not 71 divides 9421 by NAT_4:9; :: thesis:
9421 = (73 * 129) + 4 ;
hence not 73 divides 9421 by NAT_4:9; :: thesis:
9421 = (79 * 119) + 20 ;
hence not 79 divides 9421 by NAT_4:9; :: thesis:
9421 = (83 * 113) + 42 ;
hence not 83 divides 9421 by NAT_4:9; :: thesis:
9421 = (89 * 105) + 76 ;
hence not 89 divides 9421 by NAT_4:9; :: thesis:
9421 = (97 * 97) + 12 ;
hence not 97 divides 9421 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9421 & n is prime holds
not n divides 9421 by XPRIMET1:50;
hence 9421 is prime by NAT_4:14; :: thesis: