
theorem
  2957 is prime
proof
  now
    2957 = 2*1478 + 1; hence not 2 divides 2957 by NAT_4:9;
    2957 = 3*985 + 2; hence not 3 divides 2957 by NAT_4:9;
    2957 = 5*591 + 2; hence not 5 divides 2957 by NAT_4:9;
    2957 = 7*422 + 3; hence not 7 divides 2957 by NAT_4:9;
    2957 = 11*268 + 9; hence not 11 divides 2957 by NAT_4:9;
    2957 = 13*227 + 6; hence not 13 divides 2957 by NAT_4:9;
    2957 = 17*173 + 16; hence not 17 divides 2957 by NAT_4:9;
    2957 = 19*155 + 12; hence not 19 divides 2957 by NAT_4:9;
    2957 = 23*128 + 13; hence not 23 divides 2957 by NAT_4:9;
    2957 = 29*101 + 28; hence not 29 divides 2957 by NAT_4:9;
    2957 = 31*95 + 12; hence not 31 divides 2957 by NAT_4:9;
    2957 = 37*79 + 34; hence not 37 divides 2957 by NAT_4:9;
    2957 = 41*72 + 5; hence not 41 divides 2957 by NAT_4:9;
    2957 = 43*68 + 33; hence not 43 divides 2957 by NAT_4:9;
    2957 = 47*62 + 43; hence not 47 divides 2957 by NAT_4:9;
    2957 = 53*55 + 42; hence not 53 divides 2957 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2957 & n is prime
  holds not n divides 2957 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
