4987 = (2 * 2493) + 1 ;
hence not 2 divides 4987 by NAT_4:9; :: thesis:
4987 = (3 * 1662) + 1 ;
hence not 3 divides 4987 by NAT_4:9; :: thesis:
4987 = (5 * 997) + 2 ;
hence not 5 divides 4987 by NAT_4:9; :: thesis:
4987 = (7 * 712) + 3 ;
hence not 7 divides 4987 by NAT_4:9; :: thesis:
4987 = (11 * 453) + 4 ;
hence not 11 divides 4987 by NAT_4:9; :: thesis:
4987 = (13 * 383) + 8 ;
hence not 13 divides 4987 by NAT_4:9; :: thesis:
4987 = (17 * 293) + 6 ;
hence not 17 divides 4987 by NAT_4:9; :: thesis:
4987 = (19 * 262) + 9 ;
hence not 19 divides 4987 by NAT_4:9; :: thesis:
4987 = (23 * 216) + 19 ;
hence not 23 divides 4987 by NAT_4:9; :: thesis:
4987 = (29 * 171) + 28 ;
hence not 29 divides 4987 by NAT_4:9; :: thesis:
4987 = (31 * 160) + 27 ;
hence not 31 divides 4987 by NAT_4:9; :: thesis:
4987 = (37 * 134) + 29 ;
hence not 37 divides 4987 by NAT_4:9; :: thesis:
4987 = (41 * 121) + 26 ;
hence not 41 divides 4987 by NAT_4:9; :: thesis:
4987 = (43 * 115) + 42 ;
hence not 43 divides 4987 by NAT_4:9; :: thesis:
4987 = (47 * 106) + 5 ;
hence not 47 divides 4987 by NAT_4:9; :: thesis:
4987 = (53 * 94) + 5 ;
hence not 53 divides 4987 by NAT_4:9; :: thesis:
4987 = (59 * 84) + 31 ;
hence not 59 divides 4987 by NAT_4:9; :: thesis:
4987 = (61 * 81) + 46 ;
hence not 61 divides 4987 by NAT_4:9; :: thesis:
4987 = (67 * 74) + 29 ;
hence not 67 divides 4987 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 4987 & n is prime holds
not n divides 4987 by XPRIMET1:38;
hence 4987 is prime by NAT_4:14; :: thesis: