
theorem
  2879 is prime
proof
  now
    2879 = 2*1439 + 1; hence not 2 divides 2879 by NAT_4:9;
    2879 = 3*959 + 2; hence not 3 divides 2879 by NAT_4:9;
    2879 = 5*575 + 4; hence not 5 divides 2879 by NAT_4:9;
    2879 = 7*411 + 2; hence not 7 divides 2879 by NAT_4:9;
    2879 = 11*261 + 8; hence not 11 divides 2879 by NAT_4:9;
    2879 = 13*221 + 6; hence not 13 divides 2879 by NAT_4:9;
    2879 = 17*169 + 6; hence not 17 divides 2879 by NAT_4:9;
    2879 = 19*151 + 10; hence not 19 divides 2879 by NAT_4:9;
    2879 = 23*125 + 4; hence not 23 divides 2879 by NAT_4:9;
    2879 = 29*99 + 8; hence not 29 divides 2879 by NAT_4:9;
    2879 = 31*92 + 27; hence not 31 divides 2879 by NAT_4:9;
    2879 = 37*77 + 30; hence not 37 divides 2879 by NAT_4:9;
    2879 = 41*70 + 9; hence not 41 divides 2879 by NAT_4:9;
    2879 = 43*66 + 41; hence not 43 divides 2879 by NAT_4:9;
    2879 = 47*61 + 12; hence not 47 divides 2879 by NAT_4:9;
    2879 = 53*54 + 17; hence not 53 divides 2879 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2879 & n is prime
  holds not n divides 2879 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
