
theorem
  2767 is prime
proof
  now
    2767 = 2*1383 + 1; hence not 2 divides 2767 by NAT_4:9;
    2767 = 3*922 + 1; hence not 3 divides 2767 by NAT_4:9;
    2767 = 5*553 + 2; hence not 5 divides 2767 by NAT_4:9;
    2767 = 7*395 + 2; hence not 7 divides 2767 by NAT_4:9;
    2767 = 11*251 + 6; hence not 11 divides 2767 by NAT_4:9;
    2767 = 13*212 + 11; hence not 13 divides 2767 by NAT_4:9;
    2767 = 17*162 + 13; hence not 17 divides 2767 by NAT_4:9;
    2767 = 19*145 + 12; hence not 19 divides 2767 by NAT_4:9;
    2767 = 23*120 + 7; hence not 23 divides 2767 by NAT_4:9;
    2767 = 29*95 + 12; hence not 29 divides 2767 by NAT_4:9;
    2767 = 31*89 + 8; hence not 31 divides 2767 by NAT_4:9;
    2767 = 37*74 + 29; hence not 37 divides 2767 by NAT_4:9;
    2767 = 41*67 + 20; hence not 41 divides 2767 by NAT_4:9;
    2767 = 43*64 + 15; hence not 43 divides 2767 by NAT_4:9;
    2767 = 47*58 + 41; hence not 47 divides 2767 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2767 & n is prime
  holds not n divides 2767 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
