
theorem
  9521 is prime
proof
  now
    9521 = 2*4760 + 1; hence not 2 divides 9521 by NAT_4:9;
    9521 = 3*3173 + 2; hence not 3 divides 9521 by NAT_4:9;
    9521 = 5*1904 + 1; hence not 5 divides 9521 by NAT_4:9;
    9521 = 7*1360 + 1; hence not 7 divides 9521 by NAT_4:9;
    9521 = 11*865 + 6; hence not 11 divides 9521 by NAT_4:9;
    9521 = 13*732 + 5; hence not 13 divides 9521 by NAT_4:9;
    9521 = 17*560 + 1; hence not 17 divides 9521 by NAT_4:9;
    9521 = 19*501 + 2; hence not 19 divides 9521 by NAT_4:9;
    9521 = 23*413 + 22; hence not 23 divides 9521 by NAT_4:9;
    9521 = 29*328 + 9; hence not 29 divides 9521 by NAT_4:9;
    9521 = 31*307 + 4; hence not 31 divides 9521 by NAT_4:9;
    9521 = 37*257 + 12; hence not 37 divides 9521 by NAT_4:9;
    9521 = 41*232 + 9; hence not 41 divides 9521 by NAT_4:9;
    9521 = 43*221 + 18; hence not 43 divides 9521 by NAT_4:9;
    9521 = 47*202 + 27; hence not 47 divides 9521 by NAT_4:9;
    9521 = 53*179 + 34; hence not 53 divides 9521 by NAT_4:9;
    9521 = 59*161 + 22; hence not 59 divides 9521 by NAT_4:9;
    9521 = 61*156 + 5; hence not 61 divides 9521 by NAT_4:9;
    9521 = 67*142 + 7; hence not 67 divides 9521 by NAT_4:9;
    9521 = 71*134 + 7; hence not 71 divides 9521 by NAT_4:9;
    9521 = 73*130 + 31; hence not 73 divides 9521 by NAT_4:9;
    9521 = 79*120 + 41; hence not 79 divides 9521 by NAT_4:9;
    9521 = 83*114 + 59; hence not 83 divides 9521 by NAT_4:9;
    9521 = 89*106 + 87; hence not 89 divides 9521 by NAT_4:9;
    9521 = 97*98 + 15; hence not 97 divides 9521 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9521 & n is prime
  holds not n divides 9521 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
