9521 = (2 * 4760) + 1 ;
hence not 2 divides 9521 by NAT_4:9; :: thesis:
9521 = (3 * 3173) + 2 ;
hence not 3 divides 9521 by NAT_4:9; :: thesis:
9521 = (5 * 1904) + 1 ;
hence not 5 divides 9521 by NAT_4:9; :: thesis:
9521 = (7 * 1360) + 1 ;
hence not 7 divides 9521 by NAT_4:9; :: thesis:
9521 = (11 * 865) + 6 ;
hence not 11 divides 9521 by NAT_4:9; :: thesis:
9521 = (13 * 732) + 5 ;
hence not 13 divides 9521 by NAT_4:9; :: thesis:
9521 = (17 * 560) + 1 ;
hence not 17 divides 9521 by NAT_4:9; :: thesis:
9521 = (19 * 501) + 2 ;
hence not 19 divides 9521 by NAT_4:9; :: thesis:
9521 = (23 * 413) + 22 ;
hence not 23 divides 9521 by NAT_4:9; :: thesis:
9521 = (29 * 328) + 9 ;
hence not 29 divides 9521 by NAT_4:9; :: thesis:
9521 = (31 * 307) + 4 ;
hence not 31 divides 9521 by NAT_4:9; :: thesis:
9521 = (37 * 257) + 12 ;
hence not 37 divides 9521 by NAT_4:9; :: thesis:
9521 = (41 * 232) + 9 ;
hence not 41 divides 9521 by NAT_4:9; :: thesis:
9521 = (43 * 221) + 18 ;
hence not 43 divides 9521 by NAT_4:9; :: thesis:
9521 = (47 * 202) + 27 ;
hence not 47 divides 9521 by NAT_4:9; :: thesis:
9521 = (53 * 179) + 34 ;
hence not 53 divides 9521 by NAT_4:9; :: thesis:
9521 = (59 * 161) + 22 ;
hence not 59 divides 9521 by NAT_4:9; :: thesis:
9521 = (61 * 156) + 5 ;
hence not 61 divides 9521 by NAT_4:9; :: thesis:
9521 = (67 * 142) + 7 ;
hence not 67 divides 9521 by NAT_4:9; :: thesis:
9521 = (71 * 134) + 7 ;
hence not 71 divides 9521 by NAT_4:9; :: thesis:
9521 = (73 * 130) + 31 ;
hence not 73 divides 9521 by NAT_4:9; :: thesis:
9521 = (79 * 120) + 41 ;
hence not 79 divides 9521 by NAT_4:9; :: thesis:
9521 = (83 * 114) + 59 ;
hence not 83 divides 9521 by NAT_4:9; :: thesis:
9521 = (89 * 106) + 87 ;
hence not 89 divides 9521 by NAT_4:9; :: thesis:
9521 = (97 * 98) + 15 ;
hence not 97 divides 9521 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9521 & n is prime holds
not n divides 9521 by XPRIMET1:50;
hence 9521 is prime by NAT_4:14; :: thesis: