
theorem
  8951 is prime
proof
  now
    8951 = 2*4475 + 1; hence not 2 divides 8951 by NAT_4:9;
    8951 = 3*2983 + 2; hence not 3 divides 8951 by NAT_4:9;
    8951 = 5*1790 + 1; hence not 5 divides 8951 by NAT_4:9;
    8951 = 7*1278 + 5; hence not 7 divides 8951 by NAT_4:9;
    8951 = 11*813 + 8; hence not 11 divides 8951 by NAT_4:9;
    8951 = 13*688 + 7; hence not 13 divides 8951 by NAT_4:9;
    8951 = 17*526 + 9; hence not 17 divides 8951 by NAT_4:9;
    8951 = 19*471 + 2; hence not 19 divides 8951 by NAT_4:9;
    8951 = 23*389 + 4; hence not 23 divides 8951 by NAT_4:9;
    8951 = 29*308 + 19; hence not 29 divides 8951 by NAT_4:9;
    8951 = 31*288 + 23; hence not 31 divides 8951 by NAT_4:9;
    8951 = 37*241 + 34; hence not 37 divides 8951 by NAT_4:9;
    8951 = 41*218 + 13; hence not 41 divides 8951 by NAT_4:9;
    8951 = 43*208 + 7; hence not 43 divides 8951 by NAT_4:9;
    8951 = 47*190 + 21; hence not 47 divides 8951 by NAT_4:9;
    8951 = 53*168 + 47; hence not 53 divides 8951 by NAT_4:9;
    8951 = 59*151 + 42; hence not 59 divides 8951 by NAT_4:9;
    8951 = 61*146 + 45; hence not 61 divides 8951 by NAT_4:9;
    8951 = 67*133 + 40; hence not 67 divides 8951 by NAT_4:9;
    8951 = 71*126 + 5; hence not 71 divides 8951 by NAT_4:9;
    8951 = 73*122 + 45; hence not 73 divides 8951 by NAT_4:9;
    8951 = 79*113 + 24; hence not 79 divides 8951 by NAT_4:9;
    8951 = 83*107 + 70; hence not 83 divides 8951 by NAT_4:9;
    8951 = 89*100 + 51; hence not 89 divides 8951 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8951 & n is prime
  holds not n divides 8951 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
