2411 = (2 * 1205) + 1 ;
hence not 2 divides 2411 by NAT_4:9; :: thesis:
2411 = (3 * 803) + 2 ;
hence not 3 divides 2411 by NAT_4:9; :: thesis:
2411 = (5 * 482) + 1 ;
hence not 5 divides 2411 by NAT_4:9; :: thesis:
2411 = (7 * 344) + 3 ;
hence not 7 divides 2411 by NAT_4:9; :: thesis:
2411 = (11 * 219) + 2 ;
hence not 11 divides 2411 by NAT_4:9; :: thesis:
2411 = (13 * 185) + 6 ;
hence not 13 divides 2411 by NAT_4:9; :: thesis:
2411 = (17 * 141) + 14 ;
hence not 17 divides 2411 by NAT_4:9; :: thesis:
2411 = (19 * 126) + 17 ;
hence not 19 divides 2411 by NAT_4:9; :: thesis:
2411 = (23 * 104) + 19 ;
hence not 23 divides 2411 by NAT_4:9; :: thesis:
2411 = (29 * 83) + 4 ;
hence not 29 divides 2411 by NAT_4:9; :: thesis:
2411 = (31 * 77) + 24 ;
hence not 31 divides 2411 by NAT_4:9; :: thesis:
2411 = (37 * 65) + 6 ;
hence not 37 divides 2411 by NAT_4:9; :: thesis:
2411 = (41 * 58) + 33 ;
hence not 41 divides 2411 by NAT_4:9; :: thesis:
2411 = (43 * 56) + 3 ;
hence not 43 divides 2411 by NAT_4:9; :: thesis:
2411 = (47 * 51) + 14 ;
hence not 47 divides 2411 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 2411 & n is prime holds
not n divides 2411 by XPRIMET1:30;
hence 2411 is prime by NAT_4:14; :: thesis: