
theorem
  1571 is prime
proof
  now
    1571 = 2*785 + 1; hence not 2 divides 1571 by NAT_4:9;
    1571 = 3*523 + 2; hence not 3 divides 1571 by NAT_4:9;
    1571 = 5*314 + 1; hence not 5 divides 1571 by NAT_4:9;
    1571 = 7*224 + 3; hence not 7 divides 1571 by NAT_4:9;
    1571 = 11*142 + 9; hence not 11 divides 1571 by NAT_4:9;
    1571 = 13*120 + 11; hence not 13 divides 1571 by NAT_4:9;
    1571 = 17*92 + 7; hence not 17 divides 1571 by NAT_4:9;
    1571 = 19*82 + 13; hence not 19 divides 1571 by NAT_4:9;
    1571 = 23*68 + 7; hence not 23 divides 1571 by NAT_4:9;
    1571 = 29*54 + 5; hence not 29 divides 1571 by NAT_4:9;
    1571 = 31*50 + 21; hence not 31 divides 1571 by NAT_4:9;
    1571 = 37*42 + 17; hence not 37 divides 1571 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1571 & n is prime
  holds not n divides 1571 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
