
theorem
  1523 is prime
proof
  now
    1523 = 2*761 + 1; hence not 2 divides 1523 by NAT_4:9;
    1523 = 3*507 + 2; hence not 3 divides 1523 by NAT_4:9;
    1523 = 5*304 + 3; hence not 5 divides 1523 by NAT_4:9;
    1523 = 7*217 + 4; hence not 7 divides 1523 by NAT_4:9;
    1523 = 11*138 + 5; hence not 11 divides 1523 by NAT_4:9;
    1523 = 13*117 + 2; hence not 13 divides 1523 by NAT_4:9;
    1523 = 17*89 + 10; hence not 17 divides 1523 by NAT_4:9;
    1523 = 19*80 + 3; hence not 19 divides 1523 by NAT_4:9;
    1523 = 23*66 + 5; hence not 23 divides 1523 by NAT_4:9;
    1523 = 29*52 + 15; hence not 29 divides 1523 by NAT_4:9;
    1523 = 31*49 + 4; hence not 31 divides 1523 by NAT_4:9;
    1523 = 37*41 + 6; hence not 37 divides 1523 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1523 & n is prime
  holds not n divides 1523 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
