
theorem
  1511 is prime
proof
  now
    1511 = 2*755 + 1; hence not 2 divides 1511 by NAT_4:9;
    1511 = 3*503 + 2; hence not 3 divides 1511 by NAT_4:9;
    1511 = 5*302 + 1; hence not 5 divides 1511 by NAT_4:9;
    1511 = 7*215 + 6; hence not 7 divides 1511 by NAT_4:9;
    1511 = 11*137 + 4; hence not 11 divides 1511 by NAT_4:9;
    1511 = 13*116 + 3; hence not 13 divides 1511 by NAT_4:9;
    1511 = 17*88 + 15; hence not 17 divides 1511 by NAT_4:9;
    1511 = 19*79 + 10; hence not 19 divides 1511 by NAT_4:9;
    1511 = 23*65 + 16; hence not 23 divides 1511 by NAT_4:9;
    1511 = 29*52 + 3; hence not 29 divides 1511 by NAT_4:9;
    1511 = 31*48 + 23; hence not 31 divides 1511 by NAT_4:9;
    1511 = 37*40 + 31; hence not 37 divides 1511 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1511 & n is prime
  holds not n divides 1511 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
