
theorem
  1471 is prime
proof
  now
    1471 = 2*735 + 1; hence not 2 divides 1471 by NAT_4:9;
    1471 = 3*490 + 1; hence not 3 divides 1471 by NAT_4:9;
    1471 = 5*294 + 1; hence not 5 divides 1471 by NAT_4:9;
    1471 = 7*210 + 1; hence not 7 divides 1471 by NAT_4:9;
    1471 = 11*133 + 8; hence not 11 divides 1471 by NAT_4:9;
    1471 = 13*113 + 2; hence not 13 divides 1471 by NAT_4:9;
    1471 = 17*86 + 9; hence not 17 divides 1471 by NAT_4:9;
    1471 = 19*77 + 8; hence not 19 divides 1471 by NAT_4:9;
    1471 = 23*63 + 22; hence not 23 divides 1471 by NAT_4:9;
    1471 = 29*50 + 21; hence not 29 divides 1471 by NAT_4:9;
    1471 = 31*47 + 14; hence not 31 divides 1471 by NAT_4:9;
    1471 = 37*39 + 28; hence not 37 divides 1471 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1471 & n is prime
  holds not n divides 1471 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
