
theorem
  8761 is prime
proof
  now
    8761 = 2*4380 + 1; hence not 2 divides 8761 by NAT_4:9;
    8761 = 3*2920 + 1; hence not 3 divides 8761 by NAT_4:9;
    8761 = 5*1752 + 1; hence not 5 divides 8761 by NAT_4:9;
    8761 = 7*1251 + 4; hence not 7 divides 8761 by NAT_4:9;
    8761 = 11*796 + 5; hence not 11 divides 8761 by NAT_4:9;
    8761 = 13*673 + 12; hence not 13 divides 8761 by NAT_4:9;
    8761 = 17*515 + 6; hence not 17 divides 8761 by NAT_4:9;
    8761 = 19*461 + 2; hence not 19 divides 8761 by NAT_4:9;
    8761 = 23*380 + 21; hence not 23 divides 8761 by NAT_4:9;
    8761 = 29*302 + 3; hence not 29 divides 8761 by NAT_4:9;
    8761 = 31*282 + 19; hence not 31 divides 8761 by NAT_4:9;
    8761 = 37*236 + 29; hence not 37 divides 8761 by NAT_4:9;
    8761 = 41*213 + 28; hence not 41 divides 8761 by NAT_4:9;
    8761 = 43*203 + 32; hence not 43 divides 8761 by NAT_4:9;
    8761 = 47*186 + 19; hence not 47 divides 8761 by NAT_4:9;
    8761 = 53*165 + 16; hence not 53 divides 8761 by NAT_4:9;
    8761 = 59*148 + 29; hence not 59 divides 8761 by NAT_4:9;
    8761 = 61*143 + 38; hence not 61 divides 8761 by NAT_4:9;
    8761 = 67*130 + 51; hence not 67 divides 8761 by NAT_4:9;
    8761 = 71*123 + 28; hence not 71 divides 8761 by NAT_4:9;
    8761 = 73*120 + 1; hence not 73 divides 8761 by NAT_4:9;
    8761 = 79*110 + 71; hence not 79 divides 8761 by NAT_4:9;
    8761 = 83*105 + 46; hence not 83 divides 8761 by NAT_4:9;
    8761 = 89*98 + 39; hence not 89 divides 8761 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8761 & n is prime
  holds not n divides 8761 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
