
theorem
  2677 is prime
proof
  now
    2677 = 2*1338 + 1; hence not 2 divides 2677 by NAT_4:9;
    2677 = 3*892 + 1; hence not 3 divides 2677 by NAT_4:9;
    2677 = 5*535 + 2; hence not 5 divides 2677 by NAT_4:9;
    2677 = 7*382 + 3; hence not 7 divides 2677 by NAT_4:9;
    2677 = 11*243 + 4; hence not 11 divides 2677 by NAT_4:9;
    2677 = 13*205 + 12; hence not 13 divides 2677 by NAT_4:9;
    2677 = 17*157 + 8; hence not 17 divides 2677 by NAT_4:9;
    2677 = 19*140 + 17; hence not 19 divides 2677 by NAT_4:9;
    2677 = 23*116 + 9; hence not 23 divides 2677 by NAT_4:9;
    2677 = 29*92 + 9; hence not 29 divides 2677 by NAT_4:9;
    2677 = 31*86 + 11; hence not 31 divides 2677 by NAT_4:9;
    2677 = 37*72 + 13; hence not 37 divides 2677 by NAT_4:9;
    2677 = 41*65 + 12; hence not 41 divides 2677 by NAT_4:9;
    2677 = 43*62 + 11; hence not 43 divides 2677 by NAT_4:9;
    2677 = 47*56 + 45; hence not 47 divides 2677 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2677 & n is prime
  holds not n divides 2677 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
