
theorem
  1531 is prime
proof
  now
    1531 = 2*765 + 1; hence not 2 divides 1531 by NAT_4:9;
    1531 = 3*510 + 1; hence not 3 divides 1531 by NAT_4:9;
    1531 = 5*306 + 1; hence not 5 divides 1531 by NAT_4:9;
    1531 = 7*218 + 5; hence not 7 divides 1531 by NAT_4:9;
    1531 = 11*139 + 2; hence not 11 divides 1531 by NAT_4:9;
    1531 = 13*117 + 10; hence not 13 divides 1531 by NAT_4:9;
    1531 = 17*90 + 1; hence not 17 divides 1531 by NAT_4:9;
    1531 = 19*80 + 11; hence not 19 divides 1531 by NAT_4:9;
    1531 = 23*66 + 13; hence not 23 divides 1531 by NAT_4:9;
    1531 = 29*52 + 23; hence not 29 divides 1531 by NAT_4:9;
    1531 = 31*49 + 12; hence not 31 divides 1531 by NAT_4:9;
    1531 = 37*41 + 14; hence not 37 divides 1531 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1531 & n is prime
  holds not n divides 1531 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
