9839 = (2 * 4919) + 1 ;
hence not 2 divides 9839 by NAT_4:9; :: thesis:
9839 = (3 * 3279) + 2 ;
hence not 3 divides 9839 by NAT_4:9; :: thesis:
9839 = (5 * 1967) + 4 ;
hence not 5 divides 9839 by NAT_4:9; :: thesis:
9839 = (7 * 1405) + 4 ;
hence not 7 divides 9839 by NAT_4:9; :: thesis:
9839 = (11 * 894) + 5 ;
hence not 11 divides 9839 by NAT_4:9; :: thesis:
9839 = (13 * 756) + 11 ;
hence not 13 divides 9839 by NAT_4:9; :: thesis:
9839 = (17 * 578) + 13 ;
hence not 17 divides 9839 by NAT_4:9; :: thesis:
9839 = (19 * 517) + 16 ;
hence not 19 divides 9839 by NAT_4:9; :: thesis:
9839 = (23 * 427) + 18 ;
hence not 23 divides 9839 by NAT_4:9; :: thesis:
9839 = (29 * 339) + 8 ;
hence not 29 divides 9839 by NAT_4:9; :: thesis:
9839 = (31 * 317) + 12 ;
hence not 31 divides 9839 by NAT_4:9; :: thesis:
9839 = (37 * 265) + 34 ;
hence not 37 divides 9839 by NAT_4:9; :: thesis:
9839 = (41 * 239) + 40 ;
hence not 41 divides 9839 by NAT_4:9; :: thesis:
9839 = (43 * 228) + 35 ;
hence not 43 divides 9839 by NAT_4:9; :: thesis:
9839 = (47 * 209) + 16 ;
hence not 47 divides 9839 by NAT_4:9; :: thesis:
9839 = (53 * 185) + 34 ;
hence not 53 divides 9839 by NAT_4:9; :: thesis:
9839 = (59 * 166) + 45 ;
hence not 59 divides 9839 by NAT_4:9; :: thesis:
9839 = (61 * 161) + 18 ;
hence not 61 divides 9839 by NAT_4:9; :: thesis:
9839 = (67 * 146) + 57 ;
hence not 67 divides 9839 by NAT_4:9; :: thesis:
9839 = (71 * 138) + 41 ;
hence not 71 divides 9839 by NAT_4:9; :: thesis:
9839 = (73 * 134) + 57 ;
hence not 73 divides 9839 by NAT_4:9; :: thesis:
9839 = (79 * 124) + 43 ;
hence not 79 divides 9839 by NAT_4:9; :: thesis:
9839 = (83 * 118) + 45 ;
hence not 83 divides 9839 by NAT_4:9; :: thesis:
9839 = (89 * 110) + 49 ;
hence not 89 divides 9839 by NAT_4:9; :: thesis:
9839 = (97 * 101) + 42 ;
hence not 97 divides 9839 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9839 & n is prime holds
not n divides 9839 by XPRIMET1:50;
hence 9839 is prime by NAT_4:14; :: thesis: