
theorem
  2819 is prime
proof
  now
    2819 = 2*1409 + 1; hence not 2 divides 2819 by NAT_4:9;
    2819 = 3*939 + 2; hence not 3 divides 2819 by NAT_4:9;
    2819 = 5*563 + 4; hence not 5 divides 2819 by NAT_4:9;
    2819 = 7*402 + 5; hence not 7 divides 2819 by NAT_4:9;
    2819 = 11*256 + 3; hence not 11 divides 2819 by NAT_4:9;
    2819 = 13*216 + 11; hence not 13 divides 2819 by NAT_4:9;
    2819 = 17*165 + 14; hence not 17 divides 2819 by NAT_4:9;
    2819 = 19*148 + 7; hence not 19 divides 2819 by NAT_4:9;
    2819 = 23*122 + 13; hence not 23 divides 2819 by NAT_4:9;
    2819 = 29*97 + 6; hence not 29 divides 2819 by NAT_4:9;
    2819 = 31*90 + 29; hence not 31 divides 2819 by NAT_4:9;
    2819 = 37*76 + 7; hence not 37 divides 2819 by NAT_4:9;
    2819 = 41*68 + 31; hence not 41 divides 2819 by NAT_4:9;
    2819 = 43*65 + 24; hence not 43 divides 2819 by NAT_4:9;
    2819 = 47*59 + 46; hence not 47 divides 2819 by NAT_4:9;
    2819 = 53*53 + 10; hence not 53 divides 2819 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2819 & n is prime
  holds not n divides 2819 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
