2887 = (2 * 1443) + 1 ;
hence not 2 divides 2887 by NAT_4:9; :: thesis:
2887 = (3 * 962) + 1 ;
hence not 3 divides 2887 by NAT_4:9; :: thesis:
2887 = (5 * 577) + 2 ;
hence not 5 divides 2887 by NAT_4:9; :: thesis:
2887 = (7 * 412) + 3 ;
hence not 7 divides 2887 by NAT_4:9; :: thesis:
2887 = (11 * 262) + 5 ;
hence not 11 divides 2887 by NAT_4:9; :: thesis:
2887 = (13 * 222) + 1 ;
hence not 13 divides 2887 by NAT_4:9; :: thesis:
2887 = (17 * 169) + 14 ;
hence not 17 divides 2887 by NAT_4:9; :: thesis:
2887 = (19 * 151) + 18 ;
hence not 19 divides 2887 by NAT_4:9; :: thesis:
2887 = (23 * 125) + 12 ;
hence not 23 divides 2887 by NAT_4:9; :: thesis:
2887 = (29 * 99) + 16 ;
hence not 29 divides 2887 by NAT_4:9; :: thesis:
2887 = (31 * 93) + 4 ;
hence not 31 divides 2887 by NAT_4:9; :: thesis:
2887 = (37 * 78) + 1 ;
hence not 37 divides 2887 by NAT_4:9; :: thesis:
2887 = (41 * 70) + 17 ;
hence not 41 divides 2887 by NAT_4:9; :: thesis:
2887 = (43 * 67) + 6 ;
hence not 43 divides 2887 by NAT_4:9; :: thesis:
2887 = (47 * 61) + 20 ;
hence not 47 divides 2887 by NAT_4:9; :: thesis:
2887 = (53 * 54) + 25 ;
hence not 53 divides 2887 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 2887 & n is prime holds
not n divides 2887 by XPRIMET1:32;
hence 2887 is prime by NAT_4:14; :: thesis: