
theorem
  6977 is prime
proof
  now
    6977 = 2*3488 + 1; hence not 2 divides 6977 by NAT_4:9;
    6977 = 3*2325 + 2; hence not 3 divides 6977 by NAT_4:9;
    6977 = 5*1395 + 2; hence not 5 divides 6977 by NAT_4:9;
    6977 = 7*996 + 5; hence not 7 divides 6977 by NAT_4:9;
    6977 = 11*634 + 3; hence not 11 divides 6977 by NAT_4:9;
    6977 = 13*536 + 9; hence not 13 divides 6977 by NAT_4:9;
    6977 = 17*410 + 7; hence not 17 divides 6977 by NAT_4:9;
    6977 = 19*367 + 4; hence not 19 divides 6977 by NAT_4:9;
    6977 = 23*303 + 8; hence not 23 divides 6977 by NAT_4:9;
    6977 = 29*240 + 17; hence not 29 divides 6977 by NAT_4:9;
    6977 = 31*225 + 2; hence not 31 divides 6977 by NAT_4:9;
    6977 = 37*188 + 21; hence not 37 divides 6977 by NAT_4:9;
    6977 = 41*170 + 7; hence not 41 divides 6977 by NAT_4:9;
    6977 = 43*162 + 11; hence not 43 divides 6977 by NAT_4:9;
    6977 = 47*148 + 21; hence not 47 divides 6977 by NAT_4:9;
    6977 = 53*131 + 34; hence not 53 divides 6977 by NAT_4:9;
    6977 = 59*118 + 15; hence not 59 divides 6977 by NAT_4:9;
    6977 = 61*114 + 23; hence not 61 divides 6977 by NAT_4:9;
    6977 = 67*104 + 9; hence not 67 divides 6977 by NAT_4:9;
    6977 = 71*98 + 19; hence not 71 divides 6977 by NAT_4:9;
    6977 = 73*95 + 42; hence not 73 divides 6977 by NAT_4:9;
    6977 = 79*88 + 25; hence not 79 divides 6977 by NAT_4:9;
    6977 = 83*84 + 5; hence not 83 divides 6977 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6977 & n is prime
  holds not n divides 6977 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
