
theorem
  2521 is prime
proof
  now
    2521 = 2*1260 + 1; hence not 2 divides 2521 by NAT_4:9;
    2521 = 3*840 + 1; hence not 3 divides 2521 by NAT_4:9;
    2521 = 5*504 + 1; hence not 5 divides 2521 by NAT_4:9;
    2521 = 7*360 + 1; hence not 7 divides 2521 by NAT_4:9;
    2521 = 11*229 + 2; hence not 11 divides 2521 by NAT_4:9;
    2521 = 13*193 + 12; hence not 13 divides 2521 by NAT_4:9;
    2521 = 17*148 + 5; hence not 17 divides 2521 by NAT_4:9;
    2521 = 19*132 + 13; hence not 19 divides 2521 by NAT_4:9;
    2521 = 23*109 + 14; hence not 23 divides 2521 by NAT_4:9;
    2521 = 29*86 + 27; hence not 29 divides 2521 by NAT_4:9;
    2521 = 31*81 + 10; hence not 31 divides 2521 by NAT_4:9;
    2521 = 37*68 + 5; hence not 37 divides 2521 by NAT_4:9;
    2521 = 41*61 + 20; hence not 41 divides 2521 by NAT_4:9;
    2521 = 43*58 + 27; hence not 43 divides 2521 by NAT_4:9;
    2521 = 47*53 + 30; hence not 47 divides 2521 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2521 & n is prime
  holds not n divides 2521 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
