
theorem
  2939 is prime
proof
  now
    2939 = 2*1469 + 1; hence not 2 divides 2939 by NAT_4:9;
    2939 = 3*979 + 2; hence not 3 divides 2939 by NAT_4:9;
    2939 = 5*587 + 4; hence not 5 divides 2939 by NAT_4:9;
    2939 = 7*419 + 6; hence not 7 divides 2939 by NAT_4:9;
    2939 = 11*267 + 2; hence not 11 divides 2939 by NAT_4:9;
    2939 = 13*226 + 1; hence not 13 divides 2939 by NAT_4:9;
    2939 = 17*172 + 15; hence not 17 divides 2939 by NAT_4:9;
    2939 = 19*154 + 13; hence not 19 divides 2939 by NAT_4:9;
    2939 = 23*127 + 18; hence not 23 divides 2939 by NAT_4:9;
    2939 = 29*101 + 10; hence not 29 divides 2939 by NAT_4:9;
    2939 = 31*94 + 25; hence not 31 divides 2939 by NAT_4:9;
    2939 = 37*79 + 16; hence not 37 divides 2939 by NAT_4:9;
    2939 = 41*71 + 28; hence not 41 divides 2939 by NAT_4:9;
    2939 = 43*68 + 15; hence not 43 divides 2939 by NAT_4:9;
    2939 = 47*62 + 25; hence not 47 divides 2939 by NAT_4:9;
    2939 = 53*55 + 24; hence not 53 divides 2939 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2939 & n is prime
  holds not n divides 2939 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
