
theorem
  9127 is prime
proof
  now
    9127 = 2*4563 + 1; hence not 2 divides 9127 by NAT_4:9;
    9127 = 3*3042 + 1; hence not 3 divides 9127 by NAT_4:9;
    9127 = 5*1825 + 2; hence not 5 divides 9127 by NAT_4:9;
    9127 = 7*1303 + 6; hence not 7 divides 9127 by NAT_4:9;
    9127 = 11*829 + 8; hence not 11 divides 9127 by NAT_4:9;
    9127 = 13*702 + 1; hence not 13 divides 9127 by NAT_4:9;
    9127 = 17*536 + 15; hence not 17 divides 9127 by NAT_4:9;
    9127 = 19*480 + 7; hence not 19 divides 9127 by NAT_4:9;
    9127 = 23*396 + 19; hence not 23 divides 9127 by NAT_4:9;
    9127 = 29*314 + 21; hence not 29 divides 9127 by NAT_4:9;
    9127 = 31*294 + 13; hence not 31 divides 9127 by NAT_4:9;
    9127 = 37*246 + 25; hence not 37 divides 9127 by NAT_4:9;
    9127 = 41*222 + 25; hence not 41 divides 9127 by NAT_4:9;
    9127 = 43*212 + 11; hence not 43 divides 9127 by NAT_4:9;
    9127 = 47*194 + 9; hence not 47 divides 9127 by NAT_4:9;
    9127 = 53*172 + 11; hence not 53 divides 9127 by NAT_4:9;
    9127 = 59*154 + 41; hence not 59 divides 9127 by NAT_4:9;
    9127 = 61*149 + 38; hence not 61 divides 9127 by NAT_4:9;
    9127 = 67*136 + 15; hence not 67 divides 9127 by NAT_4:9;
    9127 = 71*128 + 39; hence not 71 divides 9127 by NAT_4:9;
    9127 = 73*125 + 2; hence not 73 divides 9127 by NAT_4:9;
    9127 = 79*115 + 42; hence not 79 divides 9127 by NAT_4:9;
    9127 = 83*109 + 80; hence not 83 divides 9127 by NAT_4:9;
    9127 = 89*102 + 49; hence not 89 divides 9127 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9127 & n is prime
  holds not n divides 9127 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
