
theorem
  6991 is prime
proof
  now
    6991 = 2*3495 + 1; hence not 2 divides 6991 by NAT_4:9;
    6991 = 3*2330 + 1; hence not 3 divides 6991 by NAT_4:9;
    6991 = 5*1398 + 1; hence not 5 divides 6991 by NAT_4:9;
    6991 = 7*998 + 5; hence not 7 divides 6991 by NAT_4:9;
    6991 = 11*635 + 6; hence not 11 divides 6991 by NAT_4:9;
    6991 = 13*537 + 10; hence not 13 divides 6991 by NAT_4:9;
    6991 = 17*411 + 4; hence not 17 divides 6991 by NAT_4:9;
    6991 = 19*367 + 18; hence not 19 divides 6991 by NAT_4:9;
    6991 = 23*303 + 22; hence not 23 divides 6991 by NAT_4:9;
    6991 = 29*241 + 2; hence not 29 divides 6991 by NAT_4:9;
    6991 = 31*225 + 16; hence not 31 divides 6991 by NAT_4:9;
    6991 = 37*188 + 35; hence not 37 divides 6991 by NAT_4:9;
    6991 = 41*170 + 21; hence not 41 divides 6991 by NAT_4:9;
    6991 = 43*162 + 25; hence not 43 divides 6991 by NAT_4:9;
    6991 = 47*148 + 35; hence not 47 divides 6991 by NAT_4:9;
    6991 = 53*131 + 48; hence not 53 divides 6991 by NAT_4:9;
    6991 = 59*118 + 29; hence not 59 divides 6991 by NAT_4:9;
    6991 = 61*114 + 37; hence not 61 divides 6991 by NAT_4:9;
    6991 = 67*104 + 23; hence not 67 divides 6991 by NAT_4:9;
    6991 = 71*98 + 33; hence not 71 divides 6991 by NAT_4:9;
    6991 = 73*95 + 56; hence not 73 divides 6991 by NAT_4:9;
    6991 = 79*88 + 39; hence not 79 divides 6991 by NAT_4:9;
    6991 = 83*84 + 19; hence not 83 divides 6991 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6991 & n is prime
  holds not n divides 6991 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
