
theorem
  7919 is prime
proof
  now
    7919 = 2*3959 + 1; hence not 2 divides 7919 by NAT_4:9;
    7919 = 3*2639 + 2; hence not 3 divides 7919 by NAT_4:9;
    7919 = 5*1583 + 4; hence not 5 divides 7919 by NAT_4:9;
    7919 = 7*1131 + 2; hence not 7 divides 7919 by NAT_4:9;
    7919 = 11*719 + 10; hence not 11 divides 7919 by NAT_4:9;
    7919 = 13*609 + 2; hence not 13 divides 7919 by NAT_4:9;
    7919 = 17*465 + 14; hence not 17 divides 7919 by NAT_4:9;
    7919 = 19*416 + 15; hence not 19 divides 7919 by NAT_4:9;
    7919 = 23*344 + 7; hence not 23 divides 7919 by NAT_4:9;
    7919 = 29*273 + 2; hence not 29 divides 7919 by NAT_4:9;
    7919 = 31*255 + 14; hence not 31 divides 7919 by NAT_4:9;
    7919 = 37*214 + 1; hence not 37 divides 7919 by NAT_4:9;
    7919 = 41*193 + 6; hence not 41 divides 7919 by NAT_4:9;
    7919 = 43*184 + 7; hence not 43 divides 7919 by NAT_4:9;
    7919 = 47*168 + 23; hence not 47 divides 7919 by NAT_4:9;
    7919 = 53*149 + 22; hence not 53 divides 7919 by NAT_4:9;
    7919 = 59*134 + 13; hence not 59 divides 7919 by NAT_4:9;
    7919 = 61*129 + 50; hence not 61 divides 7919 by NAT_4:9;
    7919 = 67*118 + 13; hence not 67 divides 7919 by NAT_4:9;
    7919 = 71*111 + 38; hence not 71 divides 7919 by NAT_4:9;
    7919 = 73*108 + 35; hence not 73 divides 7919 by NAT_4:9;
    7919 = 79*100 + 19; hence not 79 divides 7919 by NAT_4:9;
    7919 = 83*95 + 34; hence not 83 divides 7919 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7919 & n is prime
  holds not n divides 7919 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
