
theorem
  7927 is prime
proof
  now
    7927 = 2*3963 + 1; hence not 2 divides 7927 by NAT_4:9;
    7927 = 3*2642 + 1; hence not 3 divides 7927 by NAT_4:9;
    7927 = 5*1585 + 2; hence not 5 divides 7927 by NAT_4:9;
    7927 = 7*1132 + 3; hence not 7 divides 7927 by NAT_4:9;
    7927 = 11*720 + 7; hence not 11 divides 7927 by NAT_4:9;
    7927 = 13*609 + 10; hence not 13 divides 7927 by NAT_4:9;
    7927 = 17*466 + 5; hence not 17 divides 7927 by NAT_4:9;
    7927 = 19*417 + 4; hence not 19 divides 7927 by NAT_4:9;
    7927 = 23*344 + 15; hence not 23 divides 7927 by NAT_4:9;
    7927 = 29*273 + 10; hence not 29 divides 7927 by NAT_4:9;
    7927 = 31*255 + 22; hence not 31 divides 7927 by NAT_4:9;
    7927 = 37*214 + 9; hence not 37 divides 7927 by NAT_4:9;
    7927 = 41*193 + 14; hence not 41 divides 7927 by NAT_4:9;
    7927 = 43*184 + 15; hence not 43 divides 7927 by NAT_4:9;
    7927 = 47*168 + 31; hence not 47 divides 7927 by NAT_4:9;
    7927 = 53*149 + 30; hence not 53 divides 7927 by NAT_4:9;
    7927 = 59*134 + 21; hence not 59 divides 7927 by NAT_4:9;
    7927 = 61*129 + 58; hence not 61 divides 7927 by NAT_4:9;
    7927 = 67*118 + 21; hence not 67 divides 7927 by NAT_4:9;
    7927 = 71*111 + 46; hence not 71 divides 7927 by NAT_4:9;
    7927 = 73*108 + 43; hence not 73 divides 7927 by NAT_4:9;
    7927 = 79*100 + 27; hence not 79 divides 7927 by NAT_4:9;
    7927 = 83*95 + 42; hence not 83 divides 7927 by NAT_4:9;
    7927 = 89*89 + 6; hence not 89 divides 7927 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7927 & n is prime
  holds not n divides 7927 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
