
theorem
  6983 is prime
proof
  now
    6983 = 2*3491 + 1; hence not 2 divides 6983 by NAT_4:9;
    6983 = 3*2327 + 2; hence not 3 divides 6983 by NAT_4:9;
    6983 = 5*1396 + 3; hence not 5 divides 6983 by NAT_4:9;
    6983 = 7*997 + 4; hence not 7 divides 6983 by NAT_4:9;
    6983 = 11*634 + 9; hence not 11 divides 6983 by NAT_4:9;
    6983 = 13*537 + 2; hence not 13 divides 6983 by NAT_4:9;
    6983 = 17*410 + 13; hence not 17 divides 6983 by NAT_4:9;
    6983 = 19*367 + 10; hence not 19 divides 6983 by NAT_4:9;
    6983 = 23*303 + 14; hence not 23 divides 6983 by NAT_4:9;
    6983 = 29*240 + 23; hence not 29 divides 6983 by NAT_4:9;
    6983 = 31*225 + 8; hence not 31 divides 6983 by NAT_4:9;
    6983 = 37*188 + 27; hence not 37 divides 6983 by NAT_4:9;
    6983 = 41*170 + 13; hence not 41 divides 6983 by NAT_4:9;
    6983 = 43*162 + 17; hence not 43 divides 6983 by NAT_4:9;
    6983 = 47*148 + 27; hence not 47 divides 6983 by NAT_4:9;
    6983 = 53*131 + 40; hence not 53 divides 6983 by NAT_4:9;
    6983 = 59*118 + 21; hence not 59 divides 6983 by NAT_4:9;
    6983 = 61*114 + 29; hence not 61 divides 6983 by NAT_4:9;
    6983 = 67*104 + 15; hence not 67 divides 6983 by NAT_4:9;
    6983 = 71*98 + 25; hence not 71 divides 6983 by NAT_4:9;
    6983 = 73*95 + 48; hence not 73 divides 6983 by NAT_4:9;
    6983 = 79*88 + 31; hence not 79 divides 6983 by NAT_4:9;
    6983 = 83*84 + 11; hence not 83 divides 6983 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6983 & n is prime
  holds not n divides 6983 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
