5087 = (2 * 2543) + 1 ;
hence not 2 divides 5087 by NAT_4:9; :: thesis:
5087 = (3 * 1695) + 2 ;
hence not 3 divides 5087 by NAT_4:9; :: thesis:
5087 = (5 * 1017) + 2 ;
hence not 5 divides 5087 by NAT_4:9; :: thesis:
5087 = (7 * 726) + 5 ;
hence not 7 divides 5087 by NAT_4:9; :: thesis:
5087 = (11 * 462) + 5 ;
hence not 11 divides 5087 by NAT_4:9; :: thesis:
5087 = (13 * 391) + 4 ;
hence not 13 divides 5087 by NAT_4:9; :: thesis:
5087 = (17 * 299) + 4 ;
hence not 17 divides 5087 by NAT_4:9; :: thesis:
5087 = (19 * 267) + 14 ;
hence not 19 divides 5087 by NAT_4:9; :: thesis:
5087 = (23 * 221) + 4 ;
hence not 23 divides 5087 by NAT_4:9; :: thesis:
5087 = (29 * 175) + 12 ;
hence not 29 divides 5087 by NAT_4:9; :: thesis:
5087 = (31 * 164) + 3 ;
hence not 31 divides 5087 by NAT_4:9; :: thesis:
5087 = (37 * 137) + 18 ;
hence not 37 divides 5087 by NAT_4:9; :: thesis:
5087 = (41 * 124) + 3 ;
hence not 41 divides 5087 by NAT_4:9; :: thesis:
5087 = (43 * 118) + 13 ;
hence not 43 divides 5087 by NAT_4:9; :: thesis:
5087 = (47 * 108) + 11 ;
hence not 47 divides 5087 by NAT_4:9; :: thesis:
5087 = (53 * 95) + 52 ;
hence not 53 divides 5087 by NAT_4:9; :: thesis:
5087 = (59 * 86) + 13 ;
hence not 59 divides 5087 by NAT_4:9; :: thesis:
5087 = (61 * 83) + 24 ;
hence not 61 divides 5087 by NAT_4:9; :: thesis:
5087 = (67 * 75) + 62 ;
hence not 67 divides 5087 by NAT_4:9; :: thesis:
5087 = (71 * 71) + 46 ;
hence not 71 divides 5087 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 5087 & n is prime holds
not n divides 5087 by XPRIMET1:40;
hence 5087 is prime by NAT_4:14; :: thesis: