
theorem
  9091 is prime
proof
  now
    9091 = 2*4545 + 1; hence not 2 divides 9091 by NAT_4:9;
    9091 = 3*3030 + 1; hence not 3 divides 9091 by NAT_4:9;
    9091 = 5*1818 + 1; hence not 5 divides 9091 by NAT_4:9;
    9091 = 7*1298 + 5; hence not 7 divides 9091 by NAT_4:9;
    9091 = 11*826 + 5; hence not 11 divides 9091 by NAT_4:9;
    9091 = 13*699 + 4; hence not 13 divides 9091 by NAT_4:9;
    9091 = 17*534 + 13; hence not 17 divides 9091 by NAT_4:9;
    9091 = 19*478 + 9; hence not 19 divides 9091 by NAT_4:9;
    9091 = 23*395 + 6; hence not 23 divides 9091 by NAT_4:9;
    9091 = 29*313 + 14; hence not 29 divides 9091 by NAT_4:9;
    9091 = 31*293 + 8; hence not 31 divides 9091 by NAT_4:9;
    9091 = 37*245 + 26; hence not 37 divides 9091 by NAT_4:9;
    9091 = 41*221 + 30; hence not 41 divides 9091 by NAT_4:9;
    9091 = 43*211 + 18; hence not 43 divides 9091 by NAT_4:9;
    9091 = 47*193 + 20; hence not 47 divides 9091 by NAT_4:9;
    9091 = 53*171 + 28; hence not 53 divides 9091 by NAT_4:9;
    9091 = 59*154 + 5; hence not 59 divides 9091 by NAT_4:9;
    9091 = 61*149 + 2; hence not 61 divides 9091 by NAT_4:9;
    9091 = 67*135 + 46; hence not 67 divides 9091 by NAT_4:9;
    9091 = 71*128 + 3; hence not 71 divides 9091 by NAT_4:9;
    9091 = 73*124 + 39; hence not 73 divides 9091 by NAT_4:9;
    9091 = 79*115 + 6; hence not 79 divides 9091 by NAT_4:9;
    9091 = 83*109 + 44; hence not 83 divides 9091 by NAT_4:9;
    9091 = 89*102 + 13; hence not 89 divides 9091 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9091 & n is prime
  holds not n divides 9091 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
