
theorem
  2531 is prime
proof
  now
    2531 = 2*1265 + 1; hence not 2 divides 2531 by NAT_4:9;
    2531 = 3*843 + 2; hence not 3 divides 2531 by NAT_4:9;
    2531 = 5*506 + 1; hence not 5 divides 2531 by NAT_4:9;
    2531 = 7*361 + 4; hence not 7 divides 2531 by NAT_4:9;
    2531 = 11*230 + 1; hence not 11 divides 2531 by NAT_4:9;
    2531 = 13*194 + 9; hence not 13 divides 2531 by NAT_4:9;
    2531 = 17*148 + 15; hence not 17 divides 2531 by NAT_4:9;
    2531 = 19*133 + 4; hence not 19 divides 2531 by NAT_4:9;
    2531 = 23*110 + 1; hence not 23 divides 2531 by NAT_4:9;
    2531 = 29*87 + 8; hence not 29 divides 2531 by NAT_4:9;
    2531 = 31*81 + 20; hence not 31 divides 2531 by NAT_4:9;
    2531 = 37*68 + 15; hence not 37 divides 2531 by NAT_4:9;
    2531 = 41*61 + 30; hence not 41 divides 2531 by NAT_4:9;
    2531 = 43*58 + 37; hence not 43 divides 2531 by NAT_4:9;
    2531 = 47*53 + 40; hence not 47 divides 2531 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2531 & n is prime
  holds not n divides 2531 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
