
theorem
  1657 is prime
proof
  now
    1657 = 2*828 + 1; hence not 2 divides 1657 by NAT_4:9;
    1657 = 3*552 + 1; hence not 3 divides 1657 by NAT_4:9;
    1657 = 5*331 + 2; hence not 5 divides 1657 by NAT_4:9;
    1657 = 7*236 + 5; hence not 7 divides 1657 by NAT_4:9;
    1657 = 11*150 + 7; hence not 11 divides 1657 by NAT_4:9;
    1657 = 13*127 + 6; hence not 13 divides 1657 by NAT_4:9;
    1657 = 17*97 + 8; hence not 17 divides 1657 by NAT_4:9;
    1657 = 19*87 + 4; hence not 19 divides 1657 by NAT_4:9;
    1657 = 23*72 + 1; hence not 23 divides 1657 by NAT_4:9;
    1657 = 29*57 + 4; hence not 29 divides 1657 by NAT_4:9;
    1657 = 31*53 + 14; hence not 31 divides 1657 by NAT_4:9;
    1657 = 37*44 + 29; hence not 37 divides 1657 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1657 & n is prime
  holds not n divides 1657 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
