
theorem
  7937 is prime
proof
  now
    7937 = 2*3968 + 1; hence not 2 divides 7937 by NAT_4:9;
    7937 = 3*2645 + 2; hence not 3 divides 7937 by NAT_4:9;
    7937 = 5*1587 + 2; hence not 5 divides 7937 by NAT_4:9;
    7937 = 7*1133 + 6; hence not 7 divides 7937 by NAT_4:9;
    7937 = 11*721 + 6; hence not 11 divides 7937 by NAT_4:9;
    7937 = 13*610 + 7; hence not 13 divides 7937 by NAT_4:9;
    7937 = 17*466 + 15; hence not 17 divides 7937 by NAT_4:9;
    7937 = 19*417 + 14; hence not 19 divides 7937 by NAT_4:9;
    7937 = 23*345 + 2; hence not 23 divides 7937 by NAT_4:9;
    7937 = 29*273 + 20; hence not 29 divides 7937 by NAT_4:9;
    7937 = 31*256 + 1; hence not 31 divides 7937 by NAT_4:9;
    7937 = 37*214 + 19; hence not 37 divides 7937 by NAT_4:9;
    7937 = 41*193 + 24; hence not 41 divides 7937 by NAT_4:9;
    7937 = 43*184 + 25; hence not 43 divides 7937 by NAT_4:9;
    7937 = 47*168 + 41; hence not 47 divides 7937 by NAT_4:9;
    7937 = 53*149 + 40; hence not 53 divides 7937 by NAT_4:9;
    7937 = 59*134 + 31; hence not 59 divides 7937 by NAT_4:9;
    7937 = 61*130 + 7; hence not 61 divides 7937 by NAT_4:9;
    7937 = 67*118 + 31; hence not 67 divides 7937 by NAT_4:9;
    7937 = 71*111 + 56; hence not 71 divides 7937 by NAT_4:9;
    7937 = 73*108 + 53; hence not 73 divides 7937 by NAT_4:9;
    7937 = 79*100 + 37; hence not 79 divides 7937 by NAT_4:9;
    7937 = 83*95 + 52; hence not 83 divides 7937 by NAT_4:9;
    7937 = 89*89 + 16; hence not 89 divides 7937 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7937 & n is prime
  holds not n divides 7937 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
