
theorem
  6967 is prime
proof
  now
    6967 = 2*3483 + 1; hence not 2 divides 6967 by NAT_4:9;
    6967 = 3*2322 + 1; hence not 3 divides 6967 by NAT_4:9;
    6967 = 5*1393 + 2; hence not 5 divides 6967 by NAT_4:9;
    6967 = 7*995 + 2; hence not 7 divides 6967 by NAT_4:9;
    6967 = 11*633 + 4; hence not 11 divides 6967 by NAT_4:9;
    6967 = 13*535 + 12; hence not 13 divides 6967 by NAT_4:9;
    6967 = 17*409 + 14; hence not 17 divides 6967 by NAT_4:9;
    6967 = 19*366 + 13; hence not 19 divides 6967 by NAT_4:9;
    6967 = 23*302 + 21; hence not 23 divides 6967 by NAT_4:9;
    6967 = 29*240 + 7; hence not 29 divides 6967 by NAT_4:9;
    6967 = 31*224 + 23; hence not 31 divides 6967 by NAT_4:9;
    6967 = 37*188 + 11; hence not 37 divides 6967 by NAT_4:9;
    6967 = 41*169 + 38; hence not 41 divides 6967 by NAT_4:9;
    6967 = 43*162 + 1; hence not 43 divides 6967 by NAT_4:9;
    6967 = 47*148 + 11; hence not 47 divides 6967 by NAT_4:9;
    6967 = 53*131 + 24; hence not 53 divides 6967 by NAT_4:9;
    6967 = 59*118 + 5; hence not 59 divides 6967 by NAT_4:9;
    6967 = 61*114 + 13; hence not 61 divides 6967 by NAT_4:9;
    6967 = 67*103 + 66; hence not 67 divides 6967 by NAT_4:9;
    6967 = 71*98 + 9; hence not 71 divides 6967 by NAT_4:9;
    6967 = 73*95 + 32; hence not 73 divides 6967 by NAT_4:9;
    6967 = 79*88 + 15; hence not 79 divides 6967 by NAT_4:9;
    6967 = 83*83 + 78; hence not 83 divides 6967 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6967 & n is prime
  holds not n divides 6967 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
