9461 = (2 * 4730) + 1 ;
hence not 2 divides 9461 by NAT_4:9; :: thesis:
9461 = (3 * 3153) + 2 ;
hence not 3 divides 9461 by NAT_4:9; :: thesis:
9461 = (5 * 1892) + 1 ;
hence not 5 divides 9461 by NAT_4:9; :: thesis:
9461 = (7 * 1351) + 4 ;
hence not 7 divides 9461 by NAT_4:9; :: thesis:
9461 = (11 * 860) + 1 ;
hence not 11 divides 9461 by NAT_4:9; :: thesis:
9461 = (13 * 727) + 10 ;
hence not 13 divides 9461 by NAT_4:9; :: thesis:
9461 = (17 * 556) + 9 ;
hence not 17 divides 9461 by NAT_4:9; :: thesis:
9461 = (19 * 497) + 18 ;
hence not 19 divides 9461 by NAT_4:9; :: thesis:
9461 = (23 * 411) + 8 ;
hence not 23 divides 9461 by NAT_4:9; :: thesis:
9461 = (29 * 326) + 7 ;
hence not 29 divides 9461 by NAT_4:9; :: thesis:
9461 = (31 * 305) + 6 ;
hence not 31 divides 9461 by NAT_4:9; :: thesis:
9461 = (37 * 255) + 26 ;
hence not 37 divides 9461 by NAT_4:9; :: thesis:
9461 = (41 * 230) + 31 ;
hence not 41 divides 9461 by NAT_4:9; :: thesis:
9461 = (43 * 220) + 1 ;
hence not 43 divides 9461 by NAT_4:9; :: thesis:
9461 = (47 * 201) + 14 ;
hence not 47 divides 9461 by NAT_4:9; :: thesis:
9461 = (53 * 178) + 27 ;
hence not 53 divides 9461 by NAT_4:9; :: thesis:
9461 = (59 * 160) + 21 ;
hence not 59 divides 9461 by NAT_4:9; :: thesis:
9461 = (61 * 155) + 6 ;
hence not 61 divides 9461 by NAT_4:9; :: thesis:
9461 = (67 * 141) + 14 ;
hence not 67 divides 9461 by NAT_4:9; :: thesis:
9461 = (71 * 133) + 18 ;
hence not 71 divides 9461 by NAT_4:9; :: thesis:
9461 = (73 * 129) + 44 ;
hence not 73 divides 9461 by NAT_4:9; :: thesis:
9461 = (79 * 119) + 60 ;
hence not 79 divides 9461 by NAT_4:9; :: thesis:
9461 = (83 * 113) + 82 ;
hence not 83 divides 9461 by NAT_4:9; :: thesis:
9461 = (89 * 106) + 27 ;
hence not 89 divides 9461 by NAT_4:9; :: thesis:
9461 = (97 * 97) + 52 ;
hence not 97 divides 9461 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9461 & n is prime holds
not n divides 9461 by XPRIMET1:50;
hence 9461 is prime by NAT_4:14; :: thesis: