
theorem
  9157 is prime
proof
  now
    9157 = 2*4578 + 1; hence not 2 divides 9157 by NAT_4:9;
    9157 = 3*3052 + 1; hence not 3 divides 9157 by NAT_4:9;
    9157 = 5*1831 + 2; hence not 5 divides 9157 by NAT_4:9;
    9157 = 7*1308 + 1; hence not 7 divides 9157 by NAT_4:9;
    9157 = 11*832 + 5; hence not 11 divides 9157 by NAT_4:9;
    9157 = 13*704 + 5; hence not 13 divides 9157 by NAT_4:9;
    9157 = 17*538 + 11; hence not 17 divides 9157 by NAT_4:9;
    9157 = 19*481 + 18; hence not 19 divides 9157 by NAT_4:9;
    9157 = 23*398 + 3; hence not 23 divides 9157 by NAT_4:9;
    9157 = 29*315 + 22; hence not 29 divides 9157 by NAT_4:9;
    9157 = 31*295 + 12; hence not 31 divides 9157 by NAT_4:9;
    9157 = 37*247 + 18; hence not 37 divides 9157 by NAT_4:9;
    9157 = 41*223 + 14; hence not 41 divides 9157 by NAT_4:9;
    9157 = 43*212 + 41; hence not 43 divides 9157 by NAT_4:9;
    9157 = 47*194 + 39; hence not 47 divides 9157 by NAT_4:9;
    9157 = 53*172 + 41; hence not 53 divides 9157 by NAT_4:9;
    9157 = 59*155 + 12; hence not 59 divides 9157 by NAT_4:9;
    9157 = 61*150 + 7; hence not 61 divides 9157 by NAT_4:9;
    9157 = 67*136 + 45; hence not 67 divides 9157 by NAT_4:9;
    9157 = 71*128 + 69; hence not 71 divides 9157 by NAT_4:9;
    9157 = 73*125 + 32; hence not 73 divides 9157 by NAT_4:9;
    9157 = 79*115 + 72; hence not 79 divides 9157 by NAT_4:9;
    9157 = 83*110 + 27; hence not 83 divides 9157 by NAT_4:9;
    9157 = 89*102 + 79; hence not 89 divides 9157 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9157 & n is prime
  holds not n divides 9157 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
