
theorem
  2953 is prime
proof
  now
    2953 = 2*1476 + 1; hence not 2 divides 2953 by NAT_4:9;
    2953 = 3*984 + 1; hence not 3 divides 2953 by NAT_4:9;
    2953 = 5*590 + 3; hence not 5 divides 2953 by NAT_4:9;
    2953 = 7*421 + 6; hence not 7 divides 2953 by NAT_4:9;
    2953 = 11*268 + 5; hence not 11 divides 2953 by NAT_4:9;
    2953 = 13*227 + 2; hence not 13 divides 2953 by NAT_4:9;
    2953 = 17*173 + 12; hence not 17 divides 2953 by NAT_4:9;
    2953 = 19*155 + 8; hence not 19 divides 2953 by NAT_4:9;
    2953 = 23*128 + 9; hence not 23 divides 2953 by NAT_4:9;
    2953 = 29*101 + 24; hence not 29 divides 2953 by NAT_4:9;
    2953 = 31*95 + 8; hence not 31 divides 2953 by NAT_4:9;
    2953 = 37*79 + 30; hence not 37 divides 2953 by NAT_4:9;
    2953 = 41*72 + 1; hence not 41 divides 2953 by NAT_4:9;
    2953 = 43*68 + 29; hence not 43 divides 2953 by NAT_4:9;
    2953 = 47*62 + 39; hence not 47 divides 2953 by NAT_4:9;
    2953 = 53*55 + 38; hence not 53 divides 2953 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2953 & n is prime
  holds not n divides 2953 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
