9739 = (2 * 4869) + 1 ;
hence not 2 divides 9739 by NAT_4:9; :: thesis:
9739 = (3 * 3246) + 1 ;
hence not 3 divides 9739 by NAT_4:9; :: thesis:
9739 = (5 * 1947) + 4 ;
hence not 5 divides 9739 by NAT_4:9; :: thesis:
9739 = (7 * 1391) + 2 ;
hence not 7 divides 9739 by NAT_4:9; :: thesis:
9739 = (11 * 885) + 4 ;
hence not 11 divides 9739 by NAT_4:9; :: thesis:
9739 = (13 * 749) + 2 ;
hence not 13 divides 9739 by NAT_4:9; :: thesis:
9739 = (17 * 572) + 15 ;
hence not 17 divides 9739 by NAT_4:9; :: thesis:
9739 = (19 * 512) + 11 ;
hence not 19 divides 9739 by NAT_4:9; :: thesis:
9739 = (23 * 423) + 10 ;
hence not 23 divides 9739 by NAT_4:9; :: thesis:
9739 = (29 * 335) + 24 ;
hence not 29 divides 9739 by NAT_4:9; :: thesis:
9739 = (31 * 314) + 5 ;
hence not 31 divides 9739 by NAT_4:9; :: thesis:
9739 = (37 * 263) + 8 ;
hence not 37 divides 9739 by NAT_4:9; :: thesis:
9739 = (41 * 237) + 22 ;
hence not 41 divides 9739 by NAT_4:9; :: thesis:
9739 = (43 * 226) + 21 ;
hence not 43 divides 9739 by NAT_4:9; :: thesis:
9739 = (47 * 207) + 10 ;
hence not 47 divides 9739 by NAT_4:9; :: thesis:
9739 = (53 * 183) + 40 ;
hence not 53 divides 9739 by NAT_4:9; :: thesis:
9739 = (59 * 165) + 4 ;
hence not 59 divides 9739 by NAT_4:9; :: thesis:
9739 = (61 * 159) + 40 ;
hence not 61 divides 9739 by NAT_4:9; :: thesis:
9739 = (67 * 145) + 24 ;
hence not 67 divides 9739 by NAT_4:9; :: thesis:
9739 = (71 * 137) + 12 ;
hence not 71 divides 9739 by NAT_4:9; :: thesis:
9739 = (73 * 133) + 30 ;
hence not 73 divides 9739 by NAT_4:9; :: thesis:
9739 = (79 * 123) + 22 ;
hence not 79 divides 9739 by NAT_4:9; :: thesis:
9739 = (83 * 117) + 28 ;
hence not 83 divides 9739 by NAT_4:9; :: thesis:
9739 = (89 * 109) + 38 ;
hence not 89 divides 9739 by NAT_4:9; :: thesis:
9739 = (97 * 100) + 39 ;
hence not 97 divides 9739 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9739 & n is prime holds
not n divides 9739 by XPRIMET1:50;
hence 9739 is prime by NAT_4:14; :: thesis: