9587 = (2 * 4793) + 1 ;
hence not 2 divides 9587 by NAT_4:9; :: thesis:
9587 = (3 * 3195) + 2 ;
hence not 3 divides 9587 by NAT_4:9; :: thesis:
9587 = (5 * 1917) + 2 ;
hence not 5 divides 9587 by NAT_4:9; :: thesis:
9587 = (7 * 1369) + 4 ;
hence not 7 divides 9587 by NAT_4:9; :: thesis:
9587 = (11 * 871) + 6 ;
hence not 11 divides 9587 by NAT_4:9; :: thesis:
9587 = (13 * 737) + 6 ;
hence not 13 divides 9587 by NAT_4:9; :: thesis:
9587 = (17 * 563) + 16 ;
hence not 17 divides 9587 by NAT_4:9; :: thesis:
9587 = (19 * 504) + 11 ;
hence not 19 divides 9587 by NAT_4:9; :: thesis:
9587 = (23 * 416) + 19 ;
hence not 23 divides 9587 by NAT_4:9; :: thesis:
9587 = (29 * 330) + 17 ;
hence not 29 divides 9587 by NAT_4:9; :: thesis:
9587 = (31 * 309) + 8 ;
hence not 31 divides 9587 by NAT_4:9; :: thesis:
9587 = (37 * 259) + 4 ;
hence not 37 divides 9587 by NAT_4:9; :: thesis:
9587 = (41 * 233) + 34 ;
hence not 41 divides 9587 by NAT_4:9; :: thesis:
9587 = (43 * 222) + 41 ;
hence not 43 divides 9587 by NAT_4:9; :: thesis:
9587 = (47 * 203) + 46 ;
hence not 47 divides 9587 by NAT_4:9; :: thesis:
9587 = (53 * 180) + 47 ;
hence not 53 divides 9587 by NAT_4:9; :: thesis:
9587 = (59 * 162) + 29 ;
hence not 59 divides 9587 by NAT_4:9; :: thesis:
9587 = (61 * 157) + 10 ;
hence not 61 divides 9587 by NAT_4:9; :: thesis:
9587 = (67 * 143) + 6 ;
hence not 67 divides 9587 by NAT_4:9; :: thesis:
9587 = (71 * 135) + 2 ;
hence not 71 divides 9587 by NAT_4:9; :: thesis:
9587 = (73 * 131) + 24 ;
hence not 73 divides 9587 by NAT_4:9; :: thesis:
9587 = (79 * 121) + 28 ;
hence not 79 divides 9587 by NAT_4:9; :: thesis:
9587 = (83 * 115) + 42 ;
hence not 83 divides 9587 by NAT_4:9; :: thesis:
9587 = (89 * 107) + 64 ;
hence not 89 divides 9587 by NAT_4:9; :: thesis:
9587 = (97 * 98) + 81 ;
hence not 97 divides 9587 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9587 & n is prime holds
not n divides 9587 by XPRIMET1:50;
hence 9587 is prime by NAT_4:14; :: thesis: