
theorem
  7151 is prime
proof
  now
    7151 = 2*3575 + 1; hence not 2 divides 7151 by NAT_4:9;
    7151 = 3*2383 + 2; hence not 3 divides 7151 by NAT_4:9;
    7151 = 5*1430 + 1; hence not 5 divides 7151 by NAT_4:9;
    7151 = 7*1021 + 4; hence not 7 divides 7151 by NAT_4:9;
    7151 = 11*650 + 1; hence not 11 divides 7151 by NAT_4:9;
    7151 = 13*550 + 1; hence not 13 divides 7151 by NAT_4:9;
    7151 = 17*420 + 11; hence not 17 divides 7151 by NAT_4:9;
    7151 = 19*376 + 7; hence not 19 divides 7151 by NAT_4:9;
    7151 = 23*310 + 21; hence not 23 divides 7151 by NAT_4:9;
    7151 = 29*246 + 17; hence not 29 divides 7151 by NAT_4:9;
    7151 = 31*230 + 21; hence not 31 divides 7151 by NAT_4:9;
    7151 = 37*193 + 10; hence not 37 divides 7151 by NAT_4:9;
    7151 = 41*174 + 17; hence not 41 divides 7151 by NAT_4:9;
    7151 = 43*166 + 13; hence not 43 divides 7151 by NAT_4:9;
    7151 = 47*152 + 7; hence not 47 divides 7151 by NAT_4:9;
    7151 = 53*134 + 49; hence not 53 divides 7151 by NAT_4:9;
    7151 = 59*121 + 12; hence not 59 divides 7151 by NAT_4:9;
    7151 = 61*117 + 14; hence not 61 divides 7151 by NAT_4:9;
    7151 = 67*106 + 49; hence not 67 divides 7151 by NAT_4:9;
    7151 = 71*100 + 51; hence not 71 divides 7151 by NAT_4:9;
    7151 = 73*97 + 70; hence not 73 divides 7151 by NAT_4:9;
    7151 = 79*90 + 41; hence not 79 divides 7151 by NAT_4:9;
    7151 = 83*86 + 13; hence not 83 divides 7151 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7151 & n is prime
  holds not n divides 7151 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
