
theorem
  6971 is prime
proof
  now
    6971 = 2*3485 + 1; hence not 2 divides 6971 by NAT_4:9;
    6971 = 3*2323 + 2; hence not 3 divides 6971 by NAT_4:9;
    6971 = 5*1394 + 1; hence not 5 divides 6971 by NAT_4:9;
    6971 = 7*995 + 6; hence not 7 divides 6971 by NAT_4:9;
    6971 = 11*633 + 8; hence not 11 divides 6971 by NAT_4:9;
    6971 = 13*536 + 3; hence not 13 divides 6971 by NAT_4:9;
    6971 = 17*410 + 1; hence not 17 divides 6971 by NAT_4:9;
    6971 = 19*366 + 17; hence not 19 divides 6971 by NAT_4:9;
    6971 = 23*303 + 2; hence not 23 divides 6971 by NAT_4:9;
    6971 = 29*240 + 11; hence not 29 divides 6971 by NAT_4:9;
    6971 = 31*224 + 27; hence not 31 divides 6971 by NAT_4:9;
    6971 = 37*188 + 15; hence not 37 divides 6971 by NAT_4:9;
    6971 = 41*170 + 1; hence not 41 divides 6971 by NAT_4:9;
    6971 = 43*162 + 5; hence not 43 divides 6971 by NAT_4:9;
    6971 = 47*148 + 15; hence not 47 divides 6971 by NAT_4:9;
    6971 = 53*131 + 28; hence not 53 divides 6971 by NAT_4:9;
    6971 = 59*118 + 9; hence not 59 divides 6971 by NAT_4:9;
    6971 = 61*114 + 17; hence not 61 divides 6971 by NAT_4:9;
    6971 = 67*104 + 3; hence not 67 divides 6971 by NAT_4:9;
    6971 = 71*98 + 13; hence not 71 divides 6971 by NAT_4:9;
    6971 = 73*95 + 36; hence not 73 divides 6971 by NAT_4:9;
    6971 = 79*88 + 19; hence not 79 divides 6971 by NAT_4:9;
    6971 = 83*83 + 82; hence not 83 divides 6971 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6971 & n is prime
  holds not n divides 6971 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
