
theorem
  9341 is prime
proof
  now
    9341 = 2*4670 + 1; hence not 2 divides 9341 by NAT_4:9;
    9341 = 3*3113 + 2; hence not 3 divides 9341 by NAT_4:9;
    9341 = 5*1868 + 1; hence not 5 divides 9341 by NAT_4:9;
    9341 = 7*1334 + 3; hence not 7 divides 9341 by NAT_4:9;
    9341 = 11*849 + 2; hence not 11 divides 9341 by NAT_4:9;
    9341 = 13*718 + 7; hence not 13 divides 9341 by NAT_4:9;
    9341 = 17*549 + 8; hence not 17 divides 9341 by NAT_4:9;
    9341 = 19*491 + 12; hence not 19 divides 9341 by NAT_4:9;
    9341 = 23*406 + 3; hence not 23 divides 9341 by NAT_4:9;
    9341 = 29*322 + 3; hence not 29 divides 9341 by NAT_4:9;
    9341 = 31*301 + 10; hence not 31 divides 9341 by NAT_4:9;
    9341 = 37*252 + 17; hence not 37 divides 9341 by NAT_4:9;
    9341 = 41*227 + 34; hence not 41 divides 9341 by NAT_4:9;
    9341 = 43*217 + 10; hence not 43 divides 9341 by NAT_4:9;
    9341 = 47*198 + 35; hence not 47 divides 9341 by NAT_4:9;
    9341 = 53*176 + 13; hence not 53 divides 9341 by NAT_4:9;
    9341 = 59*158 + 19; hence not 59 divides 9341 by NAT_4:9;
    9341 = 61*153 + 8; hence not 61 divides 9341 by NAT_4:9;
    9341 = 67*139 + 28; hence not 67 divides 9341 by NAT_4:9;
    9341 = 71*131 + 40; hence not 71 divides 9341 by NAT_4:9;
    9341 = 73*127 + 70; hence not 73 divides 9341 by NAT_4:9;
    9341 = 79*118 + 19; hence not 79 divides 9341 by NAT_4:9;
    9341 = 83*112 + 45; hence not 83 divides 9341 by NAT_4:9;
    9341 = 89*104 + 85; hence not 89 divides 9341 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9341 & n is prime
  holds not n divides 9341 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
